Engine runs rough--sometimes

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I have a difficult problem to solve. Bought bike over a year ago. Have had mechanic rebuild carbs, replace old fuel system hoses, new fuel pump and fuel filter. Mechanic spent three hours going through fuel and ignition system.

Bike can run perfectly. Stop to get gas or take a short break and bike feels like it is running on three cylinders, engine is running rough. It can accelerate, though still rough and can go fast if needed. It does not seem to be a fuel delivery problem.

This usually occurs after I shut it down and restart. The idle is good, no change.

This problem is nagging and shows up for no apparent reason. I can take a long ride with no problem, yet the next time I run it the problem starts up again.

I have had many carburetor problems but I feel those are fixed. This is a California model and most of the smog devices have been removed.

Any ideas? :?