
262 S.W.3d 486 (2008)
Robert TEATE and Cynthia Mills Teate d/b/a Urban Collection
v.
CBL/PARKDALE MALL, L.P. and CBL & Associates Management, Inc. and
In re Robert Teate and Cynthia Mills Teate, d/b/a Urban Collection and Urban Collection, Inc.
Nos. 09-08-015 CV, 09-08-053 CV.
Court of Appeals of Texas, Beaumont.
Submitted May 14, 2008.
Decided August 14, 2008.
*488 Wyatt D. Snider, Jason M. Byrd, Snider & Byrd, L.L.P., Beaumont, for appellants/relator.
Karen R. Bennett, Kelli B. Smith, T. Phillip Brent, Germer Gertz, L.L.P., Beaumont, for appellee/real parties in interest.
Before GAULTNEY, KREGER, and HORTON, JJ.

OPINION
HOLLIS HORTON, Justice.
In cause number XX-XX-XXX CV, Robert Teate and Cynthia Mills Teate challenge the trial court's decision to dismiss their claims, with prejudice, as a sanction for their failure to appear for their depositions. The Teates contend that despite their failure to appear for court-ordered depositions, the dismissal of their claims is not justified under the standards established for sanctions in TransAmerican Natural Gas Corporation v. Powell, 811 S.W.2d 913, 920 (Tex.1991). We find the trial court did not abuse its discretion and affirm the judgment.

Background
CBL/Parkdale Mall, L.P. (Parkdale) entered into a written lease of space with Robert Teate "for the purpose of the retail sale of urban outerwear apparel goods, clothing line to remain consistent with `urban/hip/hop' line of apparel and for no other purpose whatsoever." By its terms, the written lease expired on September 30, 2006. On September 22, 2006, Parkdale's agent called Robert and left a message advising him that the written lease would not be renewed, and asking that he vacate the premises.
On September 29, 2006, Robert filed a request for injunctive relief with a district court in Jefferson County, Texas, against Parkdale and its managing agent, CBL & Associates Management, Inc. (CBL). In his petition for injunctive relief, Robert alleged that his written lease had expired and that since its expiration, the parties had been operating on a "month to month" basis. Robert also alleged that Parkdale had given him verbal notice to vacate on September 28 and asserted that without a month's notice he would suffer irreparable harm.
The application was not verified and contained no supporting affidavits. See TEX.R. CIV. P. 680 ("No temporary restraining order shall be granted without notice to the adverse party unless it clearly appears from specific facts shown by affidavit or by the verified complaint that immediate and irreparable injury, loss, or damage will result to the applicant before notice can be served and a hearing had thereon.") Nevertheless, the trial court entered a temporary restraining order and set a temporary injunction hearing for October 10, 2006. On October 6, 2006, Robert filed an amended application and added claims for damages and a claim for equitable relief. The amended application also named Robert's wife, Cynthia Mills [Teate], as an additional plaintiff. In addition to their claims as holdover tenants, the Teates added a claim for tortious interference of contract allegedly due to Parkdale's refusal to negotiate with them because of their race. The amended application remained unverified and also did not include any supporting affidavits.
*489 On October 10, 2006, the trial court held a temporary injunction hearing. Cynthia, Robert, and two of CBL's employees, Gwen Barry and Kurt Lundgreen, testified at the hearing. To contradict the allegation that the Teates were holdover tenants when Parkdale notified Robert to vacate the premises, Parkdale introduced the written lease executed by Robert in September 2006 that expired on September 30, 2006. Thus, while the Teates claimed they were holdover tenants, the trial court heard evidence showing that they were not. Under the September 2006 written lease, Parkdale could revoke the lease "upon not less than twenty-four (24) hours notice[.]" The Teates do not dispute they were given more than twenty-four hours notice.
During the hearing, the trial court also heard testimony regarding the parties' negotiations over a new lease that contradicted the Teates' claim that Parkdale had refused to negotiate with them. An exhibit offered by the Teates demonstrated that on September 13, 2006, Parkdale had proposed to renew the lease for a five-year term. Cynthia returned the proposal and asked for a two-year term. Parkdale subsequently leased the space to a new tenant at a significantly higher rental than the amount it proposed to the Teates.
On October 16, 2006, the trial court ruled on the requested temporary injunction and denied it. The trial court ordered that the Teates "vacate Unit B-206 at Parkdale Mall, Beaumont, Texas within thirty (30) days of the date of this Order." The trial court's order did not dispose of the Teates' other claims seeking damages.
On January 11, 2007, Parkdale's attorney sent a letter requesting the dates it could depose the Teates. Receiving no response, Parkdale's attorney sent another letter on January 31, 2007, inquiring about available dates for the Teates' depositions. Still receiving no response, Parkdale's attorney sent a third request for available dates on February 23, 2007, and advised the Teates' attorneys that Parkdale would file a motion with the court if it was unable to obtain agreed dates for the depositions.
On March 21, 2007, Parkdale filed a motion to compel the Teates to provide their depositions and also issued a notice that the court would conduct a hearing on the motion on March 30 at 9:15 a.m. At 9:00 a.m. on March 30, 2007, the Teates' attorneys filed a motion to withdraw, citing an "irreconcilable conflict" that they did not further describe.
On March 30, the trial court heard Parkdale's motion to compel, and on April 4, entered an order stating:
It is therefore, ORDERED, ADJUDGED, and DECREED that Plaintiffs Robert Teate and Cynthia Mills Teate will appear for and offer their depositions within 30 days following any hearing conducted on current counsel for Plaintiffs' Motion to Withdraw, which the Court has scheduled for April 20, 2007.
On April 20, 2007, the trial court heard the motion to withdraw and entered an order allowing the Teates' prior counsel to withdraw. Four days later, Parkdale's attorney issued notices for Cynthia's and Robert's depositions and served the notices on them by certified mail. On April 27, 2007, Cynthia and Robert sent Parkdale's attorney a letter, stating:
We would like to quash the depositions for Robert & Cynthia that you have tentatively scheduled for May 7, 2007 at 9:00 a.m. and 11:00 a.m. respectively.
We are unavailable.
They did not offer dates they would be available to be deposed or file a motion seeking any change in the trial court's prior order regarding their depositions. *490 On May 7, the Teates did not appear for their depositions, and the court reporter issued certificates of their nonappearance.
On May 21, 2007, Parkdale filed a motion for sanctions and requested that the trial court dismiss all of the Teates' claims. The Teates filed no response. The trial court subsequently granted Parkdale's motion for sanctions and ordered that Robert and Cynthia take nothing on their claims against Parkdale and CBL.
The Teates then filed an appeal and a writ of mandamus, and both assert the trial court abused its discretion in dismissing their claims as a sanction for failing to appear for their depositions. For briefing purposes, we consolidated the two proceedings and address both of them in this opinion.

Analysis
To support their abuse of discretion claim, the Teates rely on TransAmerican Natural Gas Corporation, and argue that under the circumstances here, death penalty sanctions are unjust. 811 S.W.2d 913. However, significant differences exist between the circumstances here and those in TransAmerican.
In TransAmerican, the corporation's president failed to appear for his deposition when the corporation had a motion pending in the trial court requesting that the scheduled date of the deposition be moved to another day. Id. at 915. Here, unlike the facts involved in TransAmerican, a prior court order compelled the Teates to appear for their depositions and the Teates failed to comply. When the Teates failed to appear for their depositions and failed to arrange to do so on a date prior to May 20, they violated the trial court's discovery order. Furthermore, the Teates had no pending motions that, if granted, would have protected them from providing the depositions on the dates identified in the notices.
In addition, based on the history of the proceedings prior to that time, the trial court in the case before us expressly found that the Teates "did not demonstrate a willingness to prosecute their claims against Defendants." No similar finding appears in TransAmerican, and more importantly, the Teates do not challenge the trial court's factual findings in their appeal. Unchallenged findings by the trial court are binding on the appellate court unless the record establishes to the contrary as a "matter of law" or there is "no evidence" to support the finding. McGalliard v. Kuhlmann, 722 S.W.2d 694, 696 (Tex.1986); Tinnell v. Poulson Custom Homes, Inc., No. 09-06-390 CV, 2007 WL 4973857, at *2 (Tex.App.-Beaumont, March 6, 2008, pet.denied) (mem.op.).
With the trial court's unchallenged findings in mind, we turn to the TransAmerican criteria to review whether the trial court's sanction is just. 811 S.W.2d at 917. According to the TransAmerican Court, two standards measure whether a trial court's order imposing sanctions are just. Id. "First, a direct relationship must exist between the offensive conduct and the sanction imposed." Id. "Second, just sanctions must not be excessive. The punishment should fit the crime." Id.
With respect to the relationship between the conduct and the sanction based on the circumstances presented here, we conclude the relationship is direct. The individuals who violated the court's order to appear for their depositions are the persons suffering the consequences for doing so.[1] Unlike the circumstances the *491 Court discussed in TransAmerican, the Teates did not present any evidence and did not argue before the trial court that their failure to appear was based on the advice of their attorneys. See id. at 917-18 ("The trial court must at least attempt to determine whether the offensive conduct is attributable to counsel only, or to the party only, or to both."). Under the circumstances here, the trial court could reasonably conclude that the Teates alone were responsible for the decision not to appear or provide available dates for their depositions in violation of the trial court's written order.
With respect to whether the punishment fits the crime, the trial court's order in this case expressly reflects that the court considered lesser sanctions, but concluded "that such sanctions would not properly deter Plaintiffs' conduct." When a deponent fails to appear after being directed to do so by a trial court, the Texas Rules of Civil Procedure authorize a trial court to dismiss an action, with or without prejudice. TEX.R. CIV. P. 215.2(b)(5). Thus, the penalty is within the range of punishment available to trial courts under the Rules of Procedure.
In assessing an appropriate penalty, the trial court also properly considered evidence demonstrating that the claims asserted by the Teates were without merit. For example, the trial court concluded that Parkdale had not breached the lease,[2] and had not tortiously interfered with the Teates' contract.[3] In reaching our decision about whether the trial court's decision was just, we are entitled to consider all of the proceedings that occurred prior to the trial court's entry of the order in issue. Daniel v. Kelley Oil Corp., 981 S.W.2d 230, 234 (Tex.App.-Houston [1st Dist.] 1998, pet. denied).
While trial courts are required to reasonably consider imposing lesser sanctions, when a court expressly states that it has done so, and the record contains evidence demonstrating that the claims asserted by the sanctioned party lack merit, we conclude that it is reasonable for a trial court to determine that lesser sanctions *492 would not deter a party from further abuse of the legal process. "[T]he trial court need not test the effectiveness of each available lesser sanction by actually imposing the lesser sanction on the party before issuing the death penalty; rather, the trial court must analyze the available sanctions and offer a reasoned explanation as to the appropriateness of the sanction imposed." Cire v. Cummings, 134 S.W.3d 835, 840 (Tex.2004) (reversing intermediate court's decision to set aside the trial court's death penalty sanctions, and rendering take-nothing judgment).
On this record, it is apparent that the trial court considered the Teates' claims to be wholly without merit and had ordered discovery on them. When a party asserting meritless claims continues to assert them, and then proceeds to disobey the trial court's discovery order, the trial court can reasonably conclude that the parties' claims are in fact without merit and dismiss them. TEX.R. CIV. P. 215.2(b)(5); TransAmerican, 811 S.W.2d at 918. As we find no other claims asserted in their pleadings that appear to have merit, we find no abuse of discretion in the trial court dismissing all of the claims the Teates asserted.
In conclusion, the trial court's decision to dismiss the Teates' claims was just and not excessive. The trial court's order of dismissal is affirmed. Because we have considered the Teates' appeal from a final appealable order, we dismiss the petition for mandamus in cause number XX-XX-XXX CV. Walker v. Packer, 827 S.W.2d 833, 840 (Tex.1992) (orig.proceeding) ("[M]andamus will not issue where there is an adequate remedy by appeal[.]").
AFFIRMED; PETITION DISMISSED.
NOTES
[1]  On appeal, the Teates also complain that the trial court's order dismissed the claims of Urban Collection, Inc. The trial court's order recites that the plaintiffs were Robert Teate and Cynthia Mills Teate, doing business as Urban Collection, and that "all claims and causes of action asserted by Robert Teate, Cynthia Mills Teate and Urban Collection herein are dismissed with prejudice to further filing." Because Urban Collection, Inc. was not a party to the suit when Parkdale filed its motion for sanctions, and because the parties used Urban Collection as an assumed name for the Teates' business in their pleadings, we conclude that the trial court's order of dismissal did not dispose of the claims, if any, of Urban Collection, Inc., which was identified for the first time as a party in an amended petition filed on September 10, 2007. See TEX.R. CIV. P. 28. We express no opinion concerning the standing of Urban Collection, Inc. to assert claims based on leases signed by Robert, nor do we express any opinion on the validity of the claims that Urban Collection, Inc. may attempt to assert.
[2]  The written lease that expired in September contradicted the Teates petition alleging that their written agreement had expired in July, and the evidence was not disputed that the Teates received more notice to vacate than required by that lease.
[3]  The Teates were apparently in discussions with CBL & Associates Management, Inc. to renew their lease when the written lease expired. In a letter dated September 13, 2006, CBL proposed "for Urban Collections to go permanent at Parkdale Mall," and offered to renew the lease for a five year term at an increased rent. Cynthia signed the letter, but counter-proposed a two year deal. "An acceptance must not change the terms of an offer; if it does, the offer is rejected." Gilbert v. Pettiette, 838 S.W.2d 890, 893 (Tex. App.-Houston [1st Dist.] 1992, no writ); see Chapman v. Mitsui Eng'g & Shipbuilding Co., Ltd., 781 S.W.2d 312, 316 (Tex.App.-Houston [1st Dist.] 1989, writ denied).
