We report the synthesis, crystal structure, thermal response, and electrochemical behaviour of the Prussian blue analogue (PBA) K2Cu[Fe(CN)6]. From a structural perspective, this is the most complex PBA yet characterised: its triclinic crystal structure results from an interplay of cooperative Jahn–Teller order, octahedral tilts, and a collective `slide' distortion involving K-ion displacements. These different distortions give rise to two crystallographically-distinct K-ion channels with different mobilities. Variable-temperature X-ray powder diffraction measurements show that K-ion slides are the lowest-energy distortion mechanism at play, as they are the only distortion to be switched off with increasing temperature. Electrochemically, the material operates as a K-ion cathode with a high operating voltage, and an improved initial capacity relative to higher-vacancy PBA alternatives. On charging, K+ ions are selectively removed from a single K-ion channel type and the slide distortions are again switched on and off accordingly. We discuss the functional importance of various aspects of structural complexity in this system, placing our discussion in the context of other related PBAs.