Hmm... I guess the point was missed here, but in fact what will drive the lower "Volume" on a volume control is gain.
Simply put the reason that inserting a bigger power amp for the OP was not due to it putting out maybe 3 db more on the outputs, but it probably added another 6 to 10 db "Signal Gain".
In otherwords too many people seem to think a power hungry speaker needs to go from 50 watts a channel to 250 watts a channel, when in fact most of the time using a higher input gain on the amp is what changes that volume control "Position" making it seem more powerful at lower levels.
Trust me when I say this is the case on both efficient and inefficient speakers.
From my own experience and formulated opinion most standard speakers range from about 88 to 92 db "Sensitivity".
You will see many of these same manufacturers claim a 20 watt S.E.T. amp up to 200 watt Solid state is good enough. While this may be true fact is a 30 db gain S.E.T. amp will sound more powerful even at lower volume settings than a 150 watt SS amp with just 22 db of gain.
Truth is in the Gain Chain...
My own testing has shown that if you have a standard 88 db to 92 db capable speaker that your needed gain between both the Preamp and Amp should be about 35 to 45 db. In otherwords an amp with about 25 db of gain + Preamp of lets say 14 db = 39 db is pretty much going to give you that good volume "Spread" where hitting about 12 O'clock on the dial feels good.
But if your running lets say a very high gain SS amp with 28 or 30 db, and a very High preamp which many put out 20 db, your pushing all the power up front and some people feel limited and in fact many times won't push that volume past about 9 or 10 oclock, and the signal starts to sound overdriven.
For high efficiency speakers I have found about 30 db gain across the board is good. 96 db to 110 db speakers work well with lowish gain amps around 20 to 22 db, and lowish preamps capable of being tuned down to 6 or 8 db.
Or you just go with a high gain amp 29 db - 30 db, and drop in a Passive preamp!