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This paper proposes and describes in detail a new approach to the design of very compact active microwave compressors capable of providing rectangular pulses of up to 100 ns. The approach consists in using a storage cavity, which comprises linear waveguide sections connected by tees such that the cavity geometry can be 2-D or 3-D or can be variable to allow direct space-saving integration of a compressor into a microwave source. Also presented are the scattering matrix data on uniform wave propagation along the storage cavity with little reflection and on conditions necessary for such uniformity. The S-band experiments demonstrate the capability of storage cavities with two and three parallel waveguide sections of about 1 m long to produce rectangular pulses of duration 5, 15, and 25 ns with a power gain and output power of about 16 dB, 80 MW; 15 dB, 60 MW; and 13 dB, 40 MW, respectively. Our estimates suggest that 12 waveguide sections can provide a rectangular pulse of 100 ns with a power gain 10 dB.