
659 N.W.2d 526 (2003)
STATE of Iowa, Appellee,
v.
Heidi Louise WATKINS, Appellant.
No. 01-0139.
Supreme Court of Iowa.
April 2, 2003.
*529 Michael H. Johnson of Stoller & Johnson, Spirit Lake, for appellant.
Thomas J. Miller, Attorney General, Richard Bennett and Charles Thoman, Assistant Attorneys General, and Edward W. Bjornstad, County Attorney, for appellee.
CARTER, Justice.
Defendant, Heidi Watkins, appeals from a conviction of multiple acts of child endangerment in violation of Iowa Code section 726.6A (1999). That judgment was entered following a bench trial. The court of appeals affirmed the district court judgment. We granted further review.
Defendant urges that we should reverse her conviction based on the following contentions: (1) The prosecutor acted improperly in seeking to convict her on a theory that was factually inconsistent with matters alleged and attempted to be proved in the trial of another person for the murder and sexual abuse of the same victim, (2) the district court should have granted defendant's motion for a bill of particulars, (3) defendant established at trial that she suffered from diminished capacity, (4) the trial information was unconstitutionally vague, (5) the district court should have granted a new trial, and (6) the finding of guilt was not sustained by substantial evidence. We have considered each of these contentions and conclude that the decision of the court of appeals and the district court judgment should be affirmed.
At the time of trial in August 2000, defendant was twenty-nine years of age. The evidence reveals that sometime in 1998 she began working as a foreman at her stepfather's concrete business. Working with her on this job was Jesse Wendelsdorf. At this time defendant had two children, Tyler McKnight, born August 14, 1991, and Shelby Duis, born March 29, 1997. Defendant and Wendelsdorf developed a friendship through their association at work. Gradually, their relationship became intimate, and in May 1999 Wendelsdorf began staying overnight at defendant's house. In September of that year, he moved all of his belongings into her home.
Prior to October 21, 1999, defendant used Small World Day Care as her child-care provider. That organization, which provided day care twenty-four hours a day seven days a week, provided care for Shelby during the week while defendant was working and also on some weekends. Tyler McKnight also occasionally stayed at Small World.
*530 In February 1999 the employees at Small World began noticing bruises on Shelby. As a mandatory child-abuse reporter, a Small World manager informed an investigator for the Iowa Department of Human Services (DHS). The investigator interviewed defendant and defendant's mother, each of whom told him that the bruises were sustained when Shelby ran into a door while running in a circular path throughout the house. At the suggestion of DHS, defendant placed a wooden panel across a doorway to close off this path.
Although Shelby initially interacted well with Wendelsdorf, that situation reversed itself sometime in October 1999. Thereafter, Shelby reacted negatively in Wendelsdorf's presence. By November 1999 defendant and Wendelsdorf were arguing a great deal. He wanted defendant to relinquish custody of both of her children to their respective fathers. In response to this request, defendant asked Wendelsdorf to move out. One of their mutual friends attempted to mediate their differences and apparently succeeded. Wendelsdorf remained in the home.
Although the DHS investigator found no evidence of child abuse with respect to the bruises observed in February 1999, the employees of Small World continued to be concerned. Frequently, they observed Shelby being brought to the day care center with fresh bruises. In addition, her general hygiene was not good. She had a severe diaper rash, which produced blistering sores. During the period between February 1999 and the end of that calendar year, Shelby incurred other visible injuries. On one occasion in September 1999, blood was observed in Shelby's diaper, prompting Small World employees to insist that defendant take the child to a doctor.
On October 21, 1999, Shelby came to Small World with bruises on her back and her right hand was swollen. Employees of Small World contacted the DHS investigator, who came and photographed the child. The photograph revealed red marks below Shelby's right eye and a scratch below her right ear. The investigator also observed that Shelby's right hand was red and swollen, and she had old and almost healed bruises on her back. The investigator contacted defendant and directed her to take the child to a doctor. Shelby was seen by Dr. Timothy Taylor later that day. Dr. Taylor ordered an x-ray of Shelby's right hand, which reflected a transverse fracture in the middle of the back of the hand. In Dr. Taylor's opinion, this fracture was between ten days and one-month old. Dr. Taylor also ordered a long-bone survey. Such a survey consists of x-rays of the longer bones in the arms and legs. No other fractures were found at this time.
When giving a history to Dr. Taylor on October 21, defendant told him that she had no idea how Shelby's injuries were sustained. Later, however, she told other people that the hand was injured when Shelby caught it in her crib. Dr. Taylor placed a cast on Shelby's hand and ordered that she be hospitalized overnight. He notified the DHS of the injuries he had observed and advised the agency that in his opinion defendant had given an unsatisfactory explanation. The next morning a DHS investigator met with defendant and her mother and admonished defendant concerning the numerous and continuous injuries that her child had sustained.
Shelby did not return to Small World after October 21. From that date until the first week of December, her care was provided by defendant's mother. Thereafter, defendant, who had been laid off at work, stayed at home and cared for Shelby until the child's death on January 4, 2000. On December 3 a DHS investigator came to defendant's home and observed a faint discoloration *531 near Shelby's eye, a bruise on her forehead, and old bruises on her stomach. She told defendant to have the child examined by a doctor. Thereafter, during the month of December, defendant made three separate doctor's appointments for Shelby, each of which she failed to keep. She finally took Shelby to a doctor on January 3, 2000, the day before the child's death. On that date the doctor examined a sore on the child's vagina and also a diaper-rash sore. He discovered a bruise on her face over the bridge of her nose, which was yellowish and fading.
Defendant testified that, on the morning of January 4, 2000, she awakened, signed a form that her son required for his school, and then went back to bed. She stated that she had looked in on Shelby about 10:30 a.m., saw that the child was still sleeping, and again returned to bed. According to her testimony, Wendelsdorf had gone to work that morning but returned home around noon. Wendelsdorf ate some lunch and then he and defendant engaged in sexual intercourse. Following this, Wendelsdorf received a telephone call from defendant's mother around 3:50 p.m. advising him to take care of a snow-removal job for a customer. He left the house immediately after receiving that call. Shortly after 4 p.m., defendant entered Shelby's room to check on the child. She determined that the child was not breathing and called 911. Shelby was dead when the response team arrived.
Various x-rays were taken of Shelby's body following her death. Dr. Susan Duffek, a pediatric radiologist, compared those x-rays with those taken by Dr. Taylor the previous October when the broken hand was discovered. The postdeath x-rays revealed four new broken bones in Shelby's right and left hands. Based on the appearance of aging with respect to these fractures, Dr. Duffek was able to form an opinion that these injuries had occurred on separate occasions between December 7 and December 21, 1999. Dr. Duffek also discovered several broken ribs, which, based on the appearance of aging, occurred between November 23 and December 21, 1999. Dr. Duffek testified that in her opinion none of these fractures were accidental and had been inflicted by acts of physical child abuse.
The State charged Wendelsdorf with first-degree murder with respect to Shelby's death. He was also charged with sexual abuse. Defendant was also charged with first-degree murder and, in addition, with multiple acts of child endangerment. Wendelsdorf and defendant had separate trials. He was acquitted by a jury on both the murder charge and the sexual-abuse charge. Defendant waived trial by jury and, following a bench trial, was acquitted on the murder charge but convicted on the charge of multiple acts of child endangerment.
Following the district court's findings on the issues of her guilt, defendant filed a motion for new trial. The motion was later enlarged to include a claim of newly discovered evidence. The evidence proffered in support of that motion was testimony of Wendelsdorf's most recent girlfriend that he had confessed to her that he had murdered and otherwise abused Shelby. Wendelsdorf also testified at the new-trial hearing and denied the material aspects of her testimony.
In lieu of granting a new trial, the district court invoked the provisions of Iowa Rule of Criminal Procedure 2.24(2)(c), which allows the court in a bench trial to avoid granting a new trial by reopening the record, considering the newly discovered evidence, and then rendering new findings and judgment based on the court's consideration of the enlarged record. After proceeding in this manner, the district *532 court essentially reaffirmed its initial findings concerning defendant's guilt of multiple acts of child endangerment. Other facts that may bear on the issues will be discussed in connection with our analysis of the claims made on this appeal.

I. The State's Reliance on Inconsistent Theories of Guilt in the Separate Trials of Defendant and Wendelsdorf.

Defendant argues that it is a denial of due process of law for a prosecutor, in order to convict two defendants at separate trials, to offer inconsistent theories and facts regarding the same crime. In support of that contention, she relies on the decisions of two federal courts, i.e., Smith v. Groose, 205 F.3d 1045 (8th Cir. 2000), and Thompson v. Calderon, 120 F.3d 1045 (9th Cir.1997). In Smith the prosecutor used different, and inconsistent, testimony and pretrial statements of the same witness at separate trials of two defendants. In so doing, the prosecutor both adopted and rejected each of the versions given by this witness regarding the crime. The court concluded that the prosecutor's conduct was tantamount to a denial of due process. Smith, 205 F.3d at 1048-49. In the Thompson case, a majority of the court held that due-process rights of the defendant had been violated when the prosecutor used different witnesses at different trials to materially change the prosecution's theory of who was responsible. Thompson, 120 F.3d at 1055-57.
We are convinced that these two decisions only stand for the proposition that a selective use of evidence by the prosecution in order to establish inconsistent factual contentions in separate criminal prosecutions for the same crime may be so egregious and lacking in good faith as to constitute a denial of due process. We view those situations as a narrow exception to the right of the prosecution to rely on alternative theories in criminal prosecutions albeit that they may be inconsistent. See State v. Marti, 290 N.W.2d 570, 577 (Iowa 1980) (not improper for state to pursue conflicting alternative theories as to who fired the weapon in murder prosecution resulting in finding of manslaughter). This right is particularly obvious in cases in which the evidence is not clear concerning which of two persons is the active perpetrator of the crime and which of them is an aider and abettor of the active perpetrator. Id. There is, after all, a safeguard against abuse as a result of the prosecution's burden to prove any theory it asserts by evidence beyond a reasonable doubt.
We are convinced that defendant has failed to establish denial of due process based on the State's theory of prosecution in the Wendelsdorf trial and defendant's trial. The theories of prosecution on the murder charges against the respective defendants are not a consideration in deciding this issue because both defendants were acquitted of that charge. Similarly, the sexual-abuse charge against Wendelsdorf is not a consideration because defendant was not charged with sexual abuse of Shelby. To the extent that the State may have contended at defendant's trial that she was guilty of child endangerment as a result of not preventing Wendelsdorf from sexually abusing Shelby, that contention was not inconsistent with any theory of prosecution advanced by the State in Wendelsdorf's prosecution.
With respect to the allegations of child endangerment made against defendant, they are not inconsistent with any theory of prosecution pursued against Wendelsdorf. He was not charged with child endangerment. To the extent that evidence was offered at his trial that he had physically abused Shelby, there was *533 no effort to link that evidence to the specific skeletal injuries that were the basis for the district court's findings of child endangerment on defendant's part.

II. The Denial of Defendant's Motion for a Bill of Particulars.

Defendant contends that the district court erred in failing to grant her motion for a bill of particulars seeking a statement of the precise acts on which the charge of multiple acts of child endangerment was based. She urges that the information is too imprecise because our decision in State v. Hickman, 576 N.W.2d 364, 368 (Iowa 1998), requires in prosecutions under Iowa Code section 726.6A that the state establish three separate acts "with enough precision to enable a [trier of fact] to be satisfied beyond a reasonable doubt of a time and place where each of the three acts occurred."
We have clarified the specificity requirement laid down in Hickman in State v. Yeo, 659 N.W.2d 544 (Iowa 2003). In the latter case, we recognize
this [Hickman] rule does not mean that evidence of the precise time and place of each incident or act is required, but merely means the three or more acts must be separated by time and place.
Id. at 550.
The trial information under which defendant was prosecuted (substituted second amended trial information) alleged that the State
accuses the defendant of child endangerment, a class B felony, in violation of sections 726.6(1)(a) and/or 726.6(1)(e), 726.6A, 703.2 and 703.1 of the Code of Iowa committed as follows:
Said defendant Heidi Louise Watkins commencing in February, 1999, and continuing through January 4, 2000, committed three or more acts of child endangerment, at least one of which resulted in serious injury or skeletal injury to Shelby Duis, by: acting in a manner that created a substantial risk to the physical, mental or emotional safety of Shelby Duis; and/or knowingly permitting the physical or sexual abuse of Shelby Duis.
A bill of particulars is a request for a more specific statement of the details of the offense charged. State v. Bowers, 656 N.W.2d 349, 353 (Iowa 2002); State v. Conner, 241 N.W.2d 447, 452 (Iowa 1976). Its purpose is to provide additional information that the indictment and minutes of testimony do not give. Conner, 241 N.W.2d at 452. A bill of particulars should be allowed when the charge and minutes do not sufficiently inform the defendant of the criminal acts of which she is accused. Id. Ordinarily, whether or not to grant a motion for bill of particulars rests in the discretion of the trial court, and its decision will not be disturbed absent an abuse of discretion. Marti, 290 N.W.2d at 576; State v. Gartin, 271 N.W.2d 902, 912 (Iowa 1978).
We recognized in Bowers that the specificity with which the State must charge a crime varies depending on the nature of the evidence available to the prosecution. Bowers, 656 N.W.2d at 354. If the State seeks to prove its case by evidence that separate and distinct criminal acts were perpetrated within a specified range of time, but is unable to provide evidence of the precise time and place of those criminal acts, it cannot be expected to provide more detailed information in a bill of particulars. Id.
In the present case, the State's proof of the criminal acts was based on the interpretation of the postdeath x-rays by Dr. Duffek indicating separate and distinct skeletal injuries had occurred at different *534 points of time. This evidence was supplemented by Dr. Duffek's opinion that the nature of these fractures could only have resulted from physical abuse. This evidence did not identify with precision when the physical abuse occurred. It only fixes it within a range of time. Based on our conclusions in Bowers, criminal allegations based on this evidence do not need to be more precise than the evidence itself. Other means of discovery were available to defendant for the purpose of narrowing the evidence that Dr. Duffek would provide for purposes of preparing for trial.
A bill of particulars was also not required in order to force the State to designate whether defendant or Wendelsdorf was the actual perpetrator of the acts of physical abuse on Shelby. See Marti, 290 N.W.2d at 577 (it was not improper for the state to pursue conflicting alternative theories as to who fired the weapon in murder prosecution and state could not be compelled to provide that information in bill of particulars). We find no error in the denial of the bill of particulars.

III. The Diminished Capacity Claim.

At her trial defendant proffered a defense of diminished capacity intended to show that her mental condition was such that she was unable to recognize the signs and symptoms of abuse occurring in her home. A practicing mental health counselor testified on her behalf and indicated that because defendant had herself been abused as a young child she would be more susceptible to tolerating abuse of Shelby. A witness from a batterers education facility testified that defendant suffered from posttraumatic stress disorder, borderline personality disorder, and depression. She testified that this mental status rendered defendant unable to separate herself from Wendelsdorf. A psychiatrist who had treated defendant testified that she was suffering from severe depression and posttraumatic stress disorder. He conceded, however, that she was competent to stand trial and capable of forming the intent to hurt someone. The State's expert, Dr. Michael Taylor (a physician different from the Dr. Taylor who treated Shelby on October 21), testified that defendant was capable of understanding and appreciating reality.
We conclude that the trial court was correct in failing to uphold the proffered defense of diminished responsibility for two reasons. First, the evidence was insufficient to show a diminished responsibility on defendant's part with respect to any particular volitional act. Second, this defense, as urged, had no theoretical application to this crime because the only mental element involved is that the defendant act "knowingly." See State v. McVey, 376 N.W.2d 585, 588 (Iowa 1985) (statutory requirement of acting knowingly does not introduce a mental element subject to defense of diminished responsibility).

IV. Alleged Vagueness of Section 726.6A.

Defendant urges that the statutes under which she was convicted of multiple acts of child endangerment are void for vagueness. She focuses her argument on the provisions of section 726.6(1)(a) and (e), which define the type of conduct on which the present charge was based. Section 726.6(1)(a) provides that a person commits child endangerment if that person
knowingly acts in a manner that creates a substantial risk to a child or minor's physical, mental or emotional health or safety.
Section 726.6(1)(e) provides that a person commits child endangerment when that person
knowingly permits the continuing physical or sexual abuse of a child or minor.
*535 Defendant asserts that these statutory definitions are both vague and overbroad and would allow prosecutions for taking a child hang gliding or scuba diving.
To withstand a due process challenge based on vagueness, a penal statute must define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and provide an adequate standard for those who administer the law. State v. Todd, 468 N.W.2d 462, 465 (Iowa 1991); State v. Duncan, 414 N.W.2d 91, 96 (Iowa 1987). A statute is not unconstitutionally vague if its meaning is fairly ascertainable by reference to a common and generally accepted meaning. State v. Aldrich, 231 N.W.2d 890, 894 (Iowa 1975).
We considered a vagueness challenge to section 726.6(1)(a) in State v. Anspach, 627 N.W.2d 227 (Iowa 2001). Resorting to dictionary definitions, we upheld the statute as a reasonable description of the prohibited conduct based on the nature of this crime. We are convinced that the same conclusion should be drawn with respect to section 726.6(1)(e).
A Nebraska court in State v. Crowdell, 234 Neb. 469, 451 N.W.2d 695, 695 (1990), has accurately observed:
As a matter of practicability for general application, child abuse statutes, by virtue of the nature of their subject matter and the nature of the conduct sought to be prohibited, usually contain broad and rather comprehensive language.
Crowdell, 451 N.W.2d at 699. We uphold the application of the statute in the present prosecution against defendant's claim of unconstitutional vagueness and overbreadth.

V. The Motion for New Trial.

As we have previously discussed, following the original verdict of guilt handed down against defendant, she filed a motion for new trial based on a claim of newly discovered evidence. This evidence consisted of testimony by Wendelsdorf's newly acquired girlfriend that he had confessed to her that he had murdered and otherwise abused Shelby. Acting under the authority of Iowa Rule of Criminal Procedure 2.24(2)(c), the district court, in lieu of granting a new trial, reopened the record and considered the additional testimony. Following that consideration, the court rendered new findings and judgment based on the enlarged record, which essentially reaffirmed its initial finding of guilt. Given this circumstance, defendant's claim for relief based on the newly discovered evidence can only succeed if the newly proffered evidence was such as to entitle her to acquittal as a matter of law. Clearly it did not. The district court had adequate reason to reject the new evidence on credibility grounds. The motion for new trial was properly disposed of by the district court.

VI. Sufficiency of Evidence of Guilt.

As a final matter, we consider defendant's contention that there was insufficient evidence of any actions on her part that would constitute child endangerment. She argues that, although Shelby had suffered several broken bones and bruises, the record is devoid of any evidence that these injuries could be attributed to any act on her part.
The critical findings of the district court were as follows:
This statute [section 726.6A] provides for an enhancement of the penalty if the defendant is guilty of multiple acts of child endangerment. In order for the State to prove that this code section is applicable, the State must prove the following elements beyond a reasonable doubt:

*536 1. The defendant committed three or more acts of child endangerment as defined in section 726.6.
2. The three or more acts occurred within a period of 12 months.
3. The three or more acts involved the same child.
4. One or more of the acts must have resulted in serious injury to the child or it must have resulted in a skeletal injury to a child under the age of four years.[1]
The court concludes that the State has proved each and every element of the class B felony defined in section 726.6A of the Code of Iowa. The court finds that the defendant inflicted the following injuries on Shelby:
1. The fractured second metacarpal of the right hand which occurred between October 2, 1999, and October 12, 1999.
2. The fractured third metacarpal of the right hand which occurred between December 7, 1999, and December 14, 1999.
3. The fractured second metacarpal of the left hand which occurred between December 14, 1999, and December 21, 1999.
4. The fractured third metacarpal of the left hand which occurred between December 14, 1999, and December 21, 1999.
5. Fractures to several left ribs which occurred between November 23, 1999, and December 21, 1999.
All of those acts resulted in skeletal injuries to Shelby, a child under the age of 4 years. In addition, the rib fractures come within the definition of a serious injury as that term is defined in section 702.18 of the Code.
In support of these findings, the court stated "[t]he Court gives credit to all of Dr. Duffek's testimony." Dr. Duffek had testified as to her belief that the injuries that the trial court found to have occurred were inflicted during the time periods that the trial court found and were the consequence of physical force inflicted on the child. The district court further found
after [the first week of December 1999] until the date of Shelby's death, the defendant was the sole care provider. She was with Shelby virtually twenty-four hours a day, seven days a week for the last month of Shelby's life. As noted earlier, Jesse Wendelsdorf was rarely, if ever, alone with the child. There is no evidence whatsoever to attribute Shelby's injuries to Frances Moritz (defendant's mother and the only other care taker during the period between October 21, 1999, and January 4, 2000).
The court further found:
The Court believes the defendant herself caused the broken bones described by Dr. Duffek, and even if it be conceded that Jesse Wendelsdorf caused those fractures, the defendant's attempt to coverup and hide the injuries from outside eyes, supports a finding that she knowingly permitted the continuing physical abuse of the child.
*537 If we disregard the fracture of Shelby's right hand that took place between October 2 and October 12, 1999, the remaining skeletal injuries found to have occurred all took place when defendant was exclusively responsible for Shelby's well-being. We believe that the district court's conclusion that defendant herself inflicted these injuries is supported by substantial evidence. Moreover, based on the district court's finding of her continuous proximity to the child, if Wendelsdorf had been the perpetrator of these acts, defendant would be guilty of knowingly permitting this continuing physical abuse of Shelby in violation of Iowa Code section 726.6(1)(e).
Defendant argues that the district court's finding that she personally inflicted physical abuse on Shelby was impermissible in light of the statutes referred to in the information. She notes that an earlier allegation that she had violated section 726.6(1)(b) was withdrawn. That statute provides:
1. A person who is the parent, guardian, or person having custody or control over a child ... commits child endangerment when the person does any of the following:
....

b. By an intentional act or series of intentional acts, uses unreasonable force, torture or cruelty that results in physical injury, or that is intended to cause serious injury.
Defendant urges that, given the removal of paragraph (b) of subsection 726.6(1) from the information, a finding that she herself personally committed physical abuse on the child does not state a basis for guilt under either of the paragraphs of the statute that remained after the final amendment of the trial information. We disagree with defendant's interpretation of paragraph (a) of subsection 726.6(1). If, as the district court found, defendant personally inflicted physical abuse upon the child, causing injury, that act would create a substantial risk to the child's physical, mental, or emotional health or safety. Consequently, contrary to defendant's assertion, physical abuse of Shelby by defendant would constitute conduct that is criminalized under paragraph (a). We have reviewed defendant's claims of insufficiency of proof and conclude that they are wanting.
We have considered all issues presented and conclude that the judgment of the district court should be affirmed.
AFFIRMED.
NOTES
[1]  The precise language of the statute is as follows:

A person who engages in a course of conduct including three or more acts of child endangerment as defined in section 726.6 within a period of twelve months involving the same child or a minor with a mental or physical disability, where one or more of the acts results in serious injury to the child or minor or results in a skeletal injury to a child under the age of four years, is guilty of a class "B" felony. Notwithstanding section 902.9, subsection 1, a person convicted of a violation of this section shall be confined for no more than fifty years.
Iowa Code § 726.6A.
