We describe a new family of experimental designs that extends the principle of stratified randomization to settings with continuous, constrained multivariate, and other irregular treatment spaces. Our approach is to first match units into homogeneous groups, then use Monte Carlo couplings to assign within-group treatments to be highly dispersed over the treatment space. We show that ensuring similar units receive dissimilar treatments improves estimation efficiency. The efficiency gains are proportional to the product of dispersion and match quality, where dispersion measures how spread out the assignments are relative to independent randomization. We develop a new spectral analysis showing how efficiency depends on alignment between the smoothness and shape of the estimator's influence function and the coupling's principal directions. We illustrate these designs with examples from development, behavioral, and labor economics. In particular, our empirical application uses data from a real experiment allocating savings monitors using their position within village social networks.

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