  We demonstrate a simplified method for dissipative generation of an entangled
state of two trapped-ion qubits. Our implementation produces its target state
faster and with higher fidelity than previous demonstrations of dissipative
entanglement generation and eliminates the need for auxiliary ions. The
entangled singlet state is generated in $\sim$7 ms with a fidelity of 0.949(4).
The dominant source of infidelity is photon scattering. We discuss this error
source and strategies for its mitigation.
