A dispensing closure for a squeeze bottle comprises an outer element, an intermediate element and an inner element. The outer element (3) comprises an outwardly-deflectable diaphragm (35) surrounding an outlet opening (36). The intermediate element (5) comprises an annular seat (57) underlying the outlet opening (36) of the outer element and support structure (56) for the annular seat, with an inflow opening (552) through the annular seat (57) and an outflow opening (551) through the intermediate element around the annular seat (57). The inner element comprises a blocking portion (48; 148) and support structure (46; 146) mounting the blocking portion in the closure aligned with the annular seat. The diaphragm has an inward closed position in which the annular seat of the intermediate element engages around the outlet opening to block flow, and an outwardly-deflected position in which it allows outflow through the outflow opening and outlet opening. The blocking portion of the inner element has a closed position in which it blocks the inflow opening (552) through the annular seat, and an inwardly-deflected position to allow inflow such as venting or suck-back.