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If extended to atmospheric air, soliton-assisted pulse self-compression scenarios would open unique opportunities for a long-distance transmission of high-peak-power laser pulses and remote sensing of the atmosphere. For molecular gases, general causality arguments allow dispersion anomalies only near or within molecular absorption bands. For most of these bands, dispersion anomalies are too narrowband to support compression to ultrashort pulse widths. Moreover, as a universal tendency, the steepness of dispersion profiles of molecular gases dramatically increases near the edges of molecular absorption bands, giving rise to strong ighorder dispersion, which is detrimental for the quality of ultrashort laser pulses. Whether or not such dispersion anomalies are suitable for pulse compression is far from clear. Here, we show, both experimentally and theoretically, that, despite all these difficulties, dispersion anomalies provided by molecular bands in air can provide, when combined with optical nonlinearity of air, a highly efficient self-compression of high-peak-power pulses in the mid-infrared. We demonstrate that this pulse self-compression, which occurs as a part of freebeam spatiotemporal field evolution within the regions of anomalous dispersion in air, can yield few-cycle field waveforms whose peak power is substantially higher than the peak power of the input pulses. Ultrashort high-peak-power 3.9-μm laser pulses are shown to exhibit such selfcompression dynamics when exposed to the dispersion anomaly of air induced by the asymmetric-stretch rovibrational band of carbon dioxide. Even though the group-velocity dispersion cannot be even defined as a single constant for the entire bandwidth of mid-IR laser pulses used in experiments, with all soliton transients shattered by high-order dispersion, 100– 200-GW, 100-fs, 3.9-μm laser pulses can be compressed in this regime to 35-fs subterawatt field waveforms. Unlike filamentation-assisted pulse compression, the pulse self-compression scenario identified in this work does not involve any noticeable ionization of air, enabling an ionization-loss-free whole-beam self-compression of mid-infrared laser pulses within a broad range of peak powers.