  For superconducting qubits, microwave pulses drive rotations around the Bloch
sphere. The phase of these drives can be used to generate zero-duration
arbitrary "virtual" Z-gates which, combined with two $X_{\pi/2}$ gates, can
generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates
to both improve algorithms and correct pulse errors. We perform randomized
benchmarking using a Clifford set of Hadamard and Z-gates and show that the
error per Clifford is reduced versus a set consisting of standard
finite-duration X and Y gates. Z-gates can correct unitary rotation errors for
weakly anharmonic qubits as an alternative to pulse shaping techniques such as
DRAG. We investigate leakage and show that a combination of DRAG pulse shaping
to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a
13.3~ns $X_{\pi/2}$ gate characterized by low error ($1.95[3]\times 10^{-4}$)
and low leakage ($3.1[6]\times 10^{-6}$). Ultimately leakage is limited by the
finite temperature of the qubit, but this limit is two orders-of-magnitude
smaller than pulse errors due to decoherence.
