13. A method comprising: under control of one or more computing devices configured with executable instructions, receiving a first audio signal generated by a microphone of a device residing in an environment; identifying, from the audio signal, a voice command uttered by a user in the environment; causing the device to perform a first operation specified by the voice command; identifying, from a subsequent audio signal generated by the microphone of the device, subsequent speech uttered within the environment at least partly while the device performs the first operation, the subsequent speech requesting that the device perform a second operation related to the first operation; determining whether that the user uttered the subsequent speech or whether that another user in the environment uttered the subsequent speech; interpreting the subsequent speech as a valid voice command at least partly in response to determining that the user uttered the subsequent speech; and refraining from interpreting the subsequent speech as a valid voice command at least partly in response to determining that another user in the environment uttered the subsequent speech.
16. A method as recited in claim 13 , wherein the first voice signature is based at least in part on a volume or frequency of the voice command.