As lasers become progressively higher in power, optical damage thresholds will become a limiting factor. Using the nonlinear optics of plasma may be a way to circumvent these limits. Here, we present a new self-compression mechanism for high-power, femtosecond laser pulses based on geometrical focusing and three dimensional spatiotemporal reshaping in an ionizing plasma. By propagating tightly focused, 10-mJ femtosecond laser pulses through a 100-mu m gas jet, the interplay between ionization gradients, focusing, and diffraction of the light pulse leads to stable and uniform self-compression of the pulse, while maintaining a high-energy throughput and excellent refocusability. Self-compression down to 16 fs from an original 36-fs pulse is measured using second-harmonic-generation frequency-resolved optical gating. Using this mechanism, we are able to maintain a high transmission (>88%) such that the pulse peak power is doubled. Three-dimensional numerical simulations are performed to support our interpretation of the experimental observations.