We apply laser fields to trapped atomic ions to constrain the quantum dynamics from a simultaneously applied global microwave field to an initial product state and a target entangled state. This approach comes under what has become known in the literature as "quantum Zeno dynamics" and we use it to prepare entangled states of two and three ions. With two trapped ^{9}Be^{+} ions, we obtain Bell state fidelities up to 0.990_{-5}^{+2}; with three ions, a W-state fidelity of 0.910_{-7}^{+4} is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure can be relatively insensitive to certain imperfections such as fluctuations in laser intensity.
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