I-vectors are a well-known low-dimensional representation of speaker space and are becoming increasingly popular in adaptation of state-of-the-art deep neural network (DNN) acoustic models. One advantage of i-vectors is that they can be used with very little data, for example a single utterance. However, to improve robustness of the i-vector estimates with limited data, a prior is often used. Traditionally, a standard normal prior is applied to i-vectors, which is nevertheless not well suited to the increased variability of short utterances. This paper proposes a more informative prior, derived from the training data. As well as aiming to reduce the non-Gaussian behaviour of the i-vector space, it allows prior information at different levels, for example gender, to be used. Experiments on a US English Broadcast News (BN) transcription task for speaker and utterance i-vector adaptation show that more informative priors reduce the sensitivity to the quantity of data used to estimate the i-vector. The best configuration for this task was utterance-level test i-vectors enhanced with informative priors which gave a 13% relative reduction in word error rate over the baseline (no i-vectors) and a 5% over utterance-level test i-vectors with standard prior.