Here is an example of three caps sizes. same size cigar, different wrappers.
first cap is drier and, larger. second is not as dry and, a little smaller. third is the wettest and, the smallest.
all cut with my 5/8 OD copper pipe/rotary cutter tool flat filed edge by turning outwards to make it larger and, turning it inwards to make it smaller.
Cutting the smaller cap then I need and, stretching it down around the head takes the folds out. Having it wet enables that.