Estimates of sensitivity to level differences in stop-consonant noise bursts could help designing speech-processing strategies such as dynamic-range compression and optimal consonant-vowel intensity ratio. In normal-hearing participants, we measured level-discrimination thresholds (LDTs) for the noise bursts of CVC words (/pæt/, /pæk/, and /kæt/). With /pæt/, a 2I-2AFC task measured LDTs for the pre- or post-vocalic burst in isolation or in word context; in the latter, the burst with level increments (pre or post) remained the same or varied unpredictably from trial to trial. In isolation, the 1.98–2.22 dB LDTs approached those of like-duration random noise, but increased to ≈9.0 dB for the pre-vocalic burst in-context, and more so in unpredictable-burst conditions (10.81 dB); for the post-vocalic burst the LDTs increased only slightly. To assess the role of set-size, within-trial standard, and place-of-articulation, the in-context, unpredictable-burst LDTs were measured with single- or two-observation interval 2AFC tasks presenting only /pæt/ or, randomly, /pæt/, /pæk/, or /kæt/. The context, temporal-position, predictability, and place-of-articulation effects were significant but those of within-trial standard and set size were not; for pre-vocalic bursts, LDTs were much higher (9.97 dB) for the velar than the labial consonant (4.78 dB).