We show how to significantly speed-up the encryption portion of some public-key cryptosystems by the simple expedient of allowing a sender to maintain state that is re-used across different encryptions.In particular we present stateful versions of the DHIES and Kurosawa-Desmedt schemes that each use only 1 exponentiation to encrypt, as opposed to 2 and 3 respectively in the original schemes, yielding the fastest discrete-log based public-key encryption schemes known in the random-oracle and standard models respectively. The schemes are proven to meet an appropriate extension of the standard definition of IND-CCA security that takes into account novel types of attacks possible in the stateful setting.