  We describe a protocol for the universal control of non-ideal $\pi$-periodic
superconducting qubits. Our proposal relies on a $\pi$-SQUID: a superconducting
loop formed by two $\pi$-periodic circuit elements, with an external magnetic
flux threading the circuit. The system exhibits an extensive sweet spot around
half-flux where residual $2\pi$-periodic Cooper pair tunneling is highly
suppressed. We demonstrate that universal single-qubit operations can be
realised by tuning the flux adiabatically and diabatically within this broad
sweet spot. We also assess how residual $2\pi$-periodicity in $\pi$-SQUIDs
impacts holonomic phase gates.
