An apparatus includes a shaft and an inflatable sleeve catheter. The shaft is configured for insertion through a sheath into a cavity of an organ of a patient. The inflatable sleeve catheter is fixed to a distal end of the shaft, with the inflatable sleeve catheter including (i) a resilient inner end section, which is fixed to the distal end of the shaft and is formed so as to assume a predefined shape when unconstrained, (ii) an inflatable sleeve that envelopes the inner end section, and a plurality of electrodes that are disposed over the inflatable sleeve and are configured to contact tissue.