We present a soliton effect pulse compression technique that uses self-defocusing cascaded-quadratic nonlinearities, with no fundamental limit to its scalability to high pulse energies and the capability of generating few-cycle pulses with only a frequency-doubling crystal. The conditions for which group-velocity mismatch causes an acceptable perturbation to soliton compression are analyzed and underlie optimization of the compressor. Calculations predict compression to near-single-cycle durations, with compression ratios as high as 100. Initial experiments closely agree with calculations, demonstrating compression to durations under three optical cycles (12 fs) and generation of 600 nm bandwidths.