interaction among qubits. Because of strong interactions, part of the qubit-subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a CNOT-gate or a spin transistor. Including non-symmetric contributions from couplings to ground and external control we alter the circuit slightly to compensate, and find average fidelities for our implementation of the above gates above 99.5% with operation times on the order of a nanosecond. Additionally we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.