
809 S.W.2d 914 (1991)
Bruno R. KVETINSKAS, Appellant,
v.
The STATE of Texas, Appellee.
No. C14-90-00975-CR.
Court of Appeals of Texas, Houston (14th Dist).
April 25, 1991.
S.C. Childress, Houston, for appellant.
J. Harvey Hudson, Houston, for appellee.
Before ROBERTSON, SEARS and DRAUGHN, JJ.

OPINION
DRAUGHN, Justice.
This is an appeal from a denial of appellant's application for writ of habeas corpus. Appellant alleges that he is entitled to the writ because a driving while intoxicated charge pending against him is barred by the Double Jeopardy Clause of the Fifth Amendment to the United States Constitution. We find that double jeopardy does not apply and affirm the trial court's denial of the writ.
On May 2, 1990, appellant was stopped for speeding in north Harris County by a *915 trooper with the Department of Public Safety. Following the stop, appellant was arrested for driving while intoxicated. On July 17, 1990, appellant was convicted in Justice Court for the speeding offense. Appellant then filed a writ of habeas corpus contending that the State was barred from prosecuting him for the driving while intoxicated charge under the authority of the Supreme Court's holding in Grady v. Corbin, ___ U.S. ___, 110 S.Ct. 2084, 109 L.Ed.2d 548 (1990).
To determine whether a subsequent prosecution is barred by the Double Jeopardy Clause of the Fifth Amendment, a court must first apply the test announced in Blockburger v. United States, 284 U.S. 299, 52 S.Ct. 180, 76 L.Ed. 306 (1932). Under the traditional test, a determination is made whether each offense requires proof of an additional fact that the other does not. Id. at 304, 52 S.Ct. at 182. If the offenses have identical statutory elements or one is a lesser included offense of the other, subsequent prosecution is barred on double jeopardy grounds. Grady, 110 S.Ct. at 2090. However, once an impending prosecution passes the Blockburger test, a reviewing court must then ascertain whether the government will be required to prove, as an essential element of its case, conduct constituting the offense for which the accused has already been prosecuted. The Supreme Court stated:
[T]he Double Jeopardy Clause bars any subsequent prosecution in which the government, to establish an essential element of an offense charged in that prosecution, will prove conduct that constitutes an offense for which the defendant has already been prosecuted. This is not an "actual evidence" or "same evidence" test. The critical inquiry is what conduct the State will prove, not the evidence the State will use to prove that conduct.
Id. at 2093 (emphasis added). Appellant argues that because he has already been convicted for the speeding offense, he cannot now be prosecuted for driving while intoxicated because both offenses involved the same conduct. Appellant misapprehends the Supreme Court's holding in Grady.
For the Grady prohibition to apply, the offense of speeding, for which appellant has already been prosecuted, must be an essential element of the crime of driving while intoxicated. The "conduct" referred to by the Supreme Court in Grady necessarily encompasses conduct that consists, in and of itself, of a totally separate criminal offense. There is nothing in the Supreme Court's reasoning that precludes prosecution for multiple criminal offenses stemming from the same transaction. Indeed, the Supreme Court reaffirmed its refusal to adopt a "single transaction" test regarding the Double Jeopardy Clause. Grady, 110 S.Ct. at 2094 n. 15 (citing Garrett v. United States, 471 U.S. 773, 105 S.Ct. 2407, 85 L.Ed.2d 764 (1985)).
The essential elements of the offense of driving while intoxicated are: (1) a person (2) drives or operates (3) a motor vehicle (4) in a public place (5) while intoxicated. Tex. Rev.Civ.Stat.Ann. art. 6701/-l(b) (Vernon Supp.1991); Solis v. State, 787 S.W.2d 388, 390 (Tex.Crim.App.1990). The essential elements of the offense of failure to control speed, or speeding, are: (1) a person (2) drives a vehicle (3) on a highway (4) at a speed greater than is reasonable and prudent under the existing circumstances. Tex.Rev.Civ.Stat.Ann. art. 6701rf, § 166(a) (Vernon 1977).
It may well be that appellant's intoxication contributed to his speeding. We cannot know. But we do know that speeding is not an essential element of D.W.I. A person can be prosecuted for D.W.I, regardless of the speed of his vehicle. And conversely, a driver need not be intoxicated to be prosecuted for speeding. Appellant seems to seize on the fact that the speed of his vehicle is what brought him to the attention of the officer and, therefore, his speeding somehow becomes an essential element of the D.W.I, offense so as to bar prosecution for it. We do not view Grady as requiring that result. The prohibited *916 conduct is driving a motor vehicle while intoxicated and the State does not have to prove he was speeding to make its case for D.W.I. The State need only prove that appellant was intoxicated and driving a motor vehicle in a public place. Tex.Rev.Civ. Stat.Ann. art. 6701 M(b) (Vernon Supp. 1991).
Double jeopardy does not bar appellant's prosecution for driving while intoxicated under Blockburger because each offense requires proof of an element that the other does not. Nor does Grady bar his subsequent prosecution because the separate offense of speeding is not an essential element of the offense of driving while intoxicated. We overrule appellant's sole point of error.
Accordingly, we affirm the trial court's denial of the writ of habeas corpus.
