A method and system for pulse welding provides an output pulse waveform. The waveform has at least a frequency from a range of available frequencies not limited to harmonic frequencies. The waveform provides power suitable for welding, and has a plurality of background portions alternating with a plurality of peak portions. A transition down occurs from the peak portion to the background portion with a first acceleration and a transition up occurs from the background portion to the peak portion with a second acceleration. At least one of the first and second accelerations are non-zero over at least most of the transition. The waveform is preferably created by switching an inverter. Both accelerations may be non-zero, and each transition may have two accelerations, one negative closer to the peak, and one positive closer to the background. The accelerations may be constant with opposite polarity. Preferably the process is current controlled during the transitions. The process frequency may be fixed or varying.