Premium cigars, whether parejos or figurados, will have a finished and closed head which must be cut to draw properly. In addition to having a firm grip on the cigar and the cigar cutter, it is critical to cut the head/cap at the appropriate place. The head of the cigar has a convex, or curved shape, part of which is called the shoulder. A perfect cut will leave most of the shoulder intact. It is only necessary to remove a small amount of the wrapper to expose the filler. Cutting the entire head off will probably not improve the draw, but it can cause the cigar to unravel.
Regardless of the cutter being used (piercer, punch, guillotine, scissors), the main objective is to remove enough wrapper leaf for the cigar to draw. Many cigars will draw well with just a little wrapper removed, while others may need a larger hole.
Tobacconist Tip: If you want to avoid touching the shoulder and head of a customer's cigar, hold the cigar around the band and use a sharp cigar scissor to cut the cap. Sharp scissors will give you the most control and accuracy.