Circuit Judge:
Santiago Escalante appeals the denial of his motion to suppress evidence found during a traffic stop. A sheriffs deputy stopped Escalante, ostensibly for careless driving, and discovered twenty kilos of cocaine in his car. Escalante challenges the constitutionality of the Mississippi careless driving statute and argues that the sheriffs deputy lacked probable cause to conduct the traffic stop. We affirm.
I
On the afternoon of July 11,1998, Deputy Robert Sanders was parked on the northbound side of 1-55 in Madison County, Mississippi, near the 107 mile marker. When he noticed the brake lights of Esca-lante’s car come on as it passed him, his suspicion was aroused. He also surmised that the vehicle may have been speeding, although he did not have a radar gun. He pulled onto the interstate and began to follow Escalante.
After catching up with Escalante, Sanders noticed Escalante watching him through his rear-view mirror, which caused Escalante to weave across the lane divider lines two or three times. Sanders pulled him over after following for about three miles. He testified that because Es-calante was watching him and weaving, he thought that “something was wrong” and that Escalante was engaging in “careless driving.”
During the stop, Escalante consented to a search of his car. Deputy Sanders, who had a drug-sniffing dog with him, found twenty kilograms of cocaine in a secret compartment in the trunk.
Escalante was charged with possession of cocaine with intent to distribute.1 He *680moved to suppress the drugs found by the search, arguing that the deputy did not have probable cause to stop him. Deputy Sanders argued that his stop was justified under Mississippi’s careless driving statute. The motion to suppress was denied. Escalante pleaded guilty, conditional on the appeal of the suppression ruling. He appeals.
II
Escalante argues that the Mississippi careless driving statute is unconstitutionally vague. It reads: “Any person who drives any vehicle in a careless or imprudent manner, without due regard for the width, grade, curves, corner, traffic and use of the streets and highways and all other attendant circumstances is guilty of careless driving.”2
We employ the two-part void-for-vagueness test described in City of Chicago v. Morales.3 It states:
Vagueness may invalidate a criminal law for either of two independent reasons. First, it may fail to provide the kind of notice that will enable ordinary people to understand what conduct it prohibits; second, it may authorize and even encourage arbitrary and discriminatory enforcement.4
Although the language of the statute is broad, ordinary people can understand its meaning. The Mississippi Supreme Court, in Leuer v. City of Flowood,5 has held that the terms “careless or imprudent” describe the “familiar tort law standard, requiring ... the same standard of care as a prudent person would [exercise].”6 This ubiquitous standard does not defy common understanding but relies on it. In the context of rules of the road, few people misapprehend what constitutes careful driving and what does not.
Nor does the law lack “minimal guidelines” to prevent arbitrary enforcement. Because it applies only to conduct that is negligent, such that the conduct endangers the motorist or others, the Mississippi law does not empower the police to punish whatever conduct they choose.7
The Mississippi careless driving statute is constitutional.
Ill
Escalante argues that the stop was illegal because Deputy Sanders did not have probable cause to stop him for careless driving. He contends that he did not violate the Mississippi careless driving statute, and that his weaving across the line is excusable because it was caused by Deputy Sanders following him.
The traffic stop may have been pretextual.8 But under Whren v. United States,9 a traffic stop, even if pretextual, does not violate the Fourth Amendment if *681the officer making the stop has “probable cause to believe that a traffic violation has occurred.”10 This is an objective test based on the facts known to the officer at the time of the stop, not on the motivations of the officer in making the stop. On the other hand, if it is clear that what the police observed did not constitute a violation of the cited traffic law, there is no “objective basis” for the stop, and the stop is illegal.11
As Deputy Sanders followed Escalante, Escalante weaved across the divider lines at least twice. Under Mississippi precedent, Deputy Sanders correctly believed that Escalante’s driving violated the careless driving statute.12 The Court of Appeals of Mississippi, in Guerrero v. State,13 held that a driver whose vehicle crossed over the yellow lines into the turning lane of a road “two or three times” violated the Mississippi careless driving statute, thereby justifying a traffic stop.14 In Guerrero, as in the instant case, the police were following «the defendant when they observed his vehicle cross over the lane markers; the court, however, did not discuss this fact.
Escalante contends that his weaving did not create probable cause to believe that he was driving carelessly. He argues that Deputy Sanders was following him closely, and he was paying attention to the sheriffs vehicle following him, as any prudent driver would. His weaving, he suggests, was merely the result of his divided attention.
Although the record does not establish how closely Deputy Sanders was following Escalante, Escalante’s arguments have persuasive force, and we acknowledge that this is a close case. But we recognize that Deputy Sanders could have reasonably concluded that a careful and prudent driver would not swerve out of his lane even if his attention was drawn by a law enforcement vehicle approaching from behind. Indeed, perhaps the prudent driver should be more careful to maintain his lane in such a situation. In any case, we cannot conclude that Deputy Sanders lacked probable cause to stop Escalante for careless driving.
IV
The Mississippi careless driving statute is constitutional, and Deputy Sanders had probable cause at the time of the stop to believe Escalante had violated the statute. Therefore, we hold that the stop and consequent consent search were constitutionally valid and AFFIRM the district court’s denial of Escalante’s motion to suppress.
. See 21 U.S.C.A. § 841(a)(1) (1999).
. Miss.Code Ann. § 63-3-1213 (1996).
. 527 U.S. 41, 56, 119 S.Ct. 1849, 144 L.Ed.2d 67 (1999) (plurality). Morales is the Court's most thorough discussion of void-for-vagueness in the criminal context in recent years. Although the Morales test appears in a plurality opinion, it encapsulates a longstanding test employed by the Court. See Hill v. Colorado, 530 U.S. 703, 120 S.Ct. 2480, 2498, 147 L.Ed.2d 597 (2000); Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 75 L.Ed.2d 903 (1983).
. Morales, 527 U.S. at 56, 119 S.Ct. 1849.
. 744 So.2d 266 (Miss.1999).
. Id. at 270. As state courts are the ultimate authority on issues of state law, federal courts are bound by their interpretations of state law. See Morales, 527 U.S. at 61, 119 S.Ct. 1849 ("We have no authority to construe the language of state statute more narrowly than the construction given by that State's highest court.”).
. Cf. Morales, 527 U.S. at 60-64, 119 S.Ct. 1849 (opinion of the court).
. Officer Sanders's own testimony does not conceal the fact that at the time he suspected smuggling. Although he was not carrying a radar gun, he did have a drug-sniffing dog with him.
. 517 U.S. 806, 116 S.Ct. 1769, 135 L.Ed.2d 89 (1996).
. Id. at 810, 116 S.Ct. 1769.
. United States v. Miller, 146 F.3d 274, 279 (5th Cir.1998). See also United States v. Lopez-Valdez, 178 F.3d 282, 288 (5th Cir.1999).
. "[W]e interpret the state statute the way we believe the state Supreme Court would.... If a state's highest court has not spoken on the issue, we look to the intermediate appellate courts for guidance.” Vielma v. Eureka Co., 218 F.3d 458, 462 (5th Cir.2000)(internal quotation marks omitted).
. 746 So.2d 940 (Miss.App. 1999).
. Id. at 943.