Compression of optical pulses to ultrashort pulse widths using methods of nonlinear optics is a well-established technology of modern laser science. Extending these methods to pulses with high peak powers, which become available due to the rapid progress of laser technologies, is, however, limited by the universal physical principles. With the ratio P/Pcr of the peak power of an ultrashort laser pulse, P, to the critical power of self-focusing, Pcr, playing the role of the fundamental number-of-particles integral of motion of the nonlinear Schrödinger equation, keeping this ratio constant is a key principle for the power scaling of laser-induced filamentation. Here, we show, however, that, despite all the complexity of the underlying nonlinear physics, filamentation-assisted self-compression of ultrashort laser pulses in the regime of anomalous dispersion can be scaled within a broad range of peak powers against the principle of constant P/Pcr. We identify filamentation self-compression scaling strategies whereby subcycle field waveforms with almost constant pulse widths can be generated without a dramatic degradation of beam quality within a broad range of peak powers, varying from just a few to hundreds of Pcr.