A model for predicting loudness for people with cochlear hearing loss is applied to the problem of prescribing the frequency-gain characteristic of a linear hearing aid. It is argued that a reasonable goal is to make all frequency bands of speech equally loud while achieving a comfortable overall loudness; this can maximize the proportion of the speech spectrum that is above the absolute threshold for a given loudness. In terms of the model this means that the specific loudness pattern evoked by speech of a moderate level (65 dB SPL) should be reasonably flat (equal loudness per critical band), and the overall loudness should be similar to that evoked in a normal listener by 65 dB speech (about 23 sones). The model is used to develop a new formula - the 'Cambridge formula' - for prescribing insertion gain from audiometric thresholds. It is shown that, for a fixed overall loudness of 23 sones, the Cambridge formula leads to a higher calculated articulation index than three other commonly used prescriptive methods: NAL(R), FIG6 and DSL.