I'm thinking some of this problem may be solved with speed work- the first rep is going to be harder as you've started at rest and need to fire up all your motor units to get the lift in the air. This makes your rep not just one of strength, but of explosive power, which in turn determines your rate of force development.
Dynamic Effort, or speed work, is designed to improve your power through moving submaximal weights at maximum force. For legs and back, box squats are usually done. For chest, mostly flat bench. But you can substitute other lifts if you want: normal squat, using different bars, using chains, incline or decline press, floor press,etc.
You rack 50-60% of your max on the bar and try to lift it as fast as you can. There's a law of diminishing returns on reps in a set- as you work you rbody accomodates to the load and you lose advantage. Also, if you do 4x6 instead of 3x8 you don't get as many chances to do a first rep. Usually, benching is done for 3 reps, squats for 2.
Of course, it could also be the case that your explosive power is adequate (you can move the bar fast enough) and the problem lies elsewhere. For instance you get to the bottom of the lift but don't have quite enough strength to get it started back up(called starting strength, of course). You can solve this by doing paused rep sets. Hold for 2-3 sec. at the bottom before starting back up.
Then again, it could be an indirect problem. This is where assistance work comes in. As an example, if you have trouble controlling the bar off the pins and back up again for your first rep on the bench, you may want to do heavy sets of rows for your lats. This will allow you get acheive stability and thus gain necessary control over the weight.
I'm wondering if one of the reasons we have problems with dumbells (aside from having to heave them into position,) is that we don't do much dynamic work with them. Developing power might be the answer.
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