2001 Buick Lesabre rough idle

Upon start-up, after sitting over night or for only one hour, the engine idles very rough and has surges of power. When driving off, the engine is sluggish and tries to obtain full power for the first 1/4 mile or less and then starts to run smoothly. No service engine light is produced and the local mechanic says the computer shows no problem. I disonnected / reconnected the battery cables and the engine ran smoothly for one week. Now upon start-up I can switch off and immediately restart the engine and it runs fine.

You MAY have a faulty IAC (Idle Air Control) valve.