<p>High levels of integration in intrinsically stretchable electronics require the pixel size of each component to be reduced. However, the performance of miniaturized stretchable devices, especially transistors and capacitors, is hindered by the lack of robust elastomer dielectrics that can be thinned proportionally to footprint dimensions. Here we report a crosslinking-assisted trap creation method to increase the breakdown strength of common elastomeric dielectrics. We use tailored multiarmed crosslinkers to simultaneously reduce the free volume of the elastomer network (which prevents the acceleration of charge carriers) and introduce heterogeneity (which creates deep chemical traps that tightly bind the carriers). After applying our method to nitrile rubber, it exhibits a breakdown strength of 589 kV mm⁻¹ at a thickness of 84 nm. We use the dielectric to create stretchy capacitors with high areal capacitance, stretchy transistors with a low operating voltage and a stretchy one-transistor–one-capacitor charge storage array with over 100-fold footprint reduction compared with a common elastomer dielectric. We also fabricate a high-frequency stretchy rectifier with an operating frequency up to 6.78 MHz at 100% strain, which serves as a wireless electrical switch for an implantable muscle stimulation system.</p>