
483 So.2d 500 (1986)
The STATE of Florida, Appellant,
v.
Ray Donald OGBURN, Appellee.
No. 85-805.
District Court of Appeal of Florida, Third District.
February 18, 1986.
Jim Smith, Atty. Gen., and Calianne P. Lantz, Asst. Atty. Gen., for appellant.
*501 Schweitzer & Mates and Donald Mates, Miami, for appellee.
Before SCHWARTZ, C.J., and BARKDULL and JORGENSON, JJ.
PER CURIAM.
This is a state appeal from an order of the trial court granting Donald Ogburn's motion to suppress. For the reasons which follow, we reverse.
Donald Ogburn was driving a late model Lincoln Continental with an out-of-state license plate eastbound on State Road 836 (the Dolphin Expressway). Two Florida Department of Law Enforcement agents driving in separate vehicles noticed Ogburn because his vehicle was causing a problem by moving slower than the stream of traffic. The agents had a radio conversation between themselves about Ogburn and his vehicle, concluding that Ogburn's vehicle might have been stolen. While this conversation was going on, all three vehicles continued eastbound on the expressway. As the vehicles approached an exit, Ogburn indicated with his directional signal that he was leaving the expressway and moved into the exit lane. At the last minute, he changed the course of his vehicle and re-entered the expressway. While moving from the exit lane back onto the expressway, he illegally crossed double yellow lines. Ogburn was then pulled over by one of the officers. Ogburn failed to produce a driver's license or vehicle registration. He did produce a rental car contract indicating the vehicle was rented from a South Carolina car company; however, he was not listed as an authorized driver on the contract. Ogburn was arrested for failure to produce a valid driver's license. When the other officer looked inside the car, he found a brown bag under the driver's seat. The bag contained cocaine.
The trial court granted the motion to suppress on the stated basis that "the testimony is clear that the officer had no founded suspicion to stop the Defendant's car as he was under the mistaken belief that the car was stolen." Whether the agent's suspicion that the car had been stolen was a "founded suspicion" is irrelevant because there is no question that he observed Ogburn commit a traffic violation before effectuating the stop. A lawful investigatory stop for a traffic violation is not invalidated by the fact that an officer would not have stopped a defendant but for the suspicion that the defendant was involved in criminal activity. State v. Irvin, 483 So.2d 461 (Fla. 5th DCA 1986); Bascoy v. State, 424 So.2d 80 (Fla. 3d DCA 1982); Crummie v. State, 367 So.2d 1106 (Fla. 3d DCA 1979). Thus, the stop of Ogburn was proper. Because Ogburn was properly arrested for failing to produce his driver's license, the subsequent search of his vehicle, which revealed contraband cocaine, was lawful. See New York v. Belton, 453 U.S. 454, 101 S.Ct. 2860, 69 L.Ed.2d 768, reh'g denied, 453 U.S. 950, 102 S.Ct. 26, 69 L.Ed.2d 1036 (1981); State v. Padron, 425 So.2d 644 (Fla. 3d DCA 1983), approved, 449 So.2d 811 (Fla. 1984).
The order of suppression is accordingly reversed, and this cause is remanded for further proceedings.
Reversed and remanded for further proceedings.
