A method of and an apparatus for drilling blind vias with selectable tapers in multilayer electronic circuits permit forming electrical connections between layers while maintaining quality and throughput. The method relies on recognizing that the top diameter of the via and the bottom diameter of the via, which define the taper, are functions of two separate sets of equations. Simultaneous solution of these equations yields a solution space that enables optimization of throughput while maintaining selected taper and quality using temporally unmodified Q-switched CO2 laser pulses with identical pulse parameters. Real time pulse tailoring is not required; therefore, system complexity and cost may be reduced.