Despite the fact that a quantum measurement generally disturbs the state of a quantum system, recent work of Seth Lloyd and collaborators demonstrates that a sender and receiver can communicate at the Holevo rate even when the receiver performs a large number of sequential measurements to determine the message of the sender. The present work contributes to this direction, by addressing three questions that have arisen from the work on sequential decoding. First, we show that Pranab Sen's non-commutative union bound applies for a sequence of general measurements (not merely projective ones). Next, we use this result to prove that sequential decoding works well even in the "one-shot" regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. Finally, we demonstrate two ways in which a receiver can recover a state close to the original state after it has been decoded by a sequence of measurements that each succeed with high probability. The second of these methods will be useful in realizing an efficient decoder for fully quantum polar codes, should a method ever be found to realize an efficient decoder for classical-quantum polar codes. This work is available as arXiv:1303.0808.