Recent studies have been revisiting whole words as the basic modelling unit in speech recognition and query applications, instead of phonetic units. Such whole-word segmental systems rely on a function that maps a variable-length speech segment to a vector in a fixed-dimensional space; the resulting acoustic word embeddings need to allow for accurate discrimination between different word types, directly in the embedding space. We compare several old and new approaches in a word discrimination task. Our best approach uses side information in the form of known word pairs to train a Siamese convolutional neural network (CNN): a pair of tied networks that take two speech segments as input and produce their embeddings, trained with a hinge loss that separates same-word pairs and different-word pairs by some margin. A word classifier CNN performs similarly, but requires much stronger supervision. Both types of CNNs yield large improvements over the best previously published results on the word discrimination task.