  The three-spin-$1/2$ decoherence-free subsystem defines a logical qubit
protected from collective noise and supports exchange-only universal gates.
Such logical qubits are well-suited for implementation with
electrically-defined quantum dots. Exact exchange-only entangling logical gates
exist but are challenging to construct and understand. We use a decoupling
strategy to obtain straightforward approximate entangling gates. A benefit of
the strategy is that if the physical spins are aligned, then it can implement
evolution under entangling Hamiltonians. Hamiltonians expressible as linear
combinations of logical Pauli products not involving $\sigma_y$ can be
implemented directly. Self-inverse gates that are constructible from these
Hamiltonians, such as the CNOT, can be implemented without the assumption on
the physical spins. We compare the control complexity of implementing CNOT to
previous methods and find that the complexity for fault-tolerant fidelities is
competitive.
