As virtual assistants have become more diverse and specialized, so has the demand for application or brand-specific wake words. However, the wake-word-specific datasets typically used to train wake-word detectors are costly to create. In this paper, we explore two techniques to leverage acoustic modeling data for large-vocabulary speech recognition to improve a purpose-built wake-word detector: transfer learning and knowledge distillation. We also explore how these techniques interact with time-synchronous training targets to improve detection latency. Experiments are presented on the open-source "Hey Snips” dataset and a more challenging in-house far-field dataset. Using phone-synchronous targets and knowledge distillation from a large acoustic model, we are able to improve accuracy across dataset sizes for both datasets while reducing latency.