Difficulties understanding speech in background noise is often a pivotal reason to seek treatment for hearing loss. In the clinic, ‘difficulty’ and ‘clarity’ are commonly regarded as perceptually opposite valences; hearing aids should alleviate the perceived ‘difficulty’ by making sounds ‘clearer’. Acoustically, speech intelligibility depends primarily on the signal-to-noise ratio (SNR). In the context of hearing aid evaluations, it is important to understand how and when differences in SNR are noticed. While just-noticeable differences (JNDs) in SNR have been studied for differences in clarity, it remained unclear if different valence or prior knowledge of the speech can affect JNDs. This study measured SNR JNDs when framed as ’clarity’ or ‘difficulty’ and also with and without signal familiarity provided by auditory primes. In a two-by-two repeated-measures design, the SNR JNDs of twenty-five participants with varying hearing abilities were measured in a 2I/2AFC task. In each trial, two intervals with a randomly chosen sentence in speech-spectrum noise were presented in random order: one at each participant’s speech reception threshold (SNR50), and the other at the SNR50 plus an SNR increment (0, 1, 2, 4 or 8 dB). In the prime conditions, participants listened to the same sentence without noise just prior to the two intervals. Participants were asked to select the interval they perceived as ‘more clear’ in the clarity frame or ‘more difficult’ in the difficulty frame. Mean SNR JNDs in the clarity frame were 2.8 and 3.1 dB with and without prime, respectively, and in the difficulty frame 3.3 and 4.0 dB with and without prime, respectively. Across prime conditions, framing had a significant effect on SNR JNDs; average JNDs were greater for the difficulty than the clarity frame. Individual JNDs for difficulty and clarity were positively associated but not significantly correlated in any condition. Although priming reduced individual differences, this method had no significant effect on mean SNR JNDs. Whether the target was in the first or second interval affected participants’ decisions in all conditions; without primes, there was a preference for the second interval in the clarity frame, and for the first interval in the difficulty frame. This bias was weakened and inverted by priming. The results suggest that the framing of speech intelligibility benefits as well as prior SNRs have an influence on how SNR differences are perceived, and hence should be considered in the clinic when discussing and addressing patients’ hearing-in-noise needs.