Direct integration of translation model (TM) probabilities into a language model (LM) with the purpose of improving automatic speech recognition (ASR) of spoken translations typically requires a number of complex operations for each sentence. Many if not all of the LM probabilities need to be updated, the model needs to be renormalized and the ASR system needs to load a new, updated LM for each sentence. In computer-aided translation environments the time loss induced by these complex operations seriously reduces the potential of ASR as an efficient input method. In this paper we present a novel LM adaptation technique that drastically reduces the complexity of each of these operations. The technique consists of LM probability updates using exponential weights based on TM probabilities for each sentence and does not enforce probability renormalization. Instead of storing each resulting language model in its entirety, we only store the update weights which also reduces disk storage and loading time during ASR. Experiments on Dutch read speech translated from English show that both disk storage and recognition time drop dramatically compared to a baseline system that employs a more conventional way of updating the LM.