In processing connected speech, listeners must parse a highly variable signal. We investigate processing of a particular type of production variability, namely epenthetic stops between nasals and obstruents. Using a phoneme monitoring task and a dictation task, we test listeners' perception of epenthetic stops (which are not part of the string of segments intended by the speaker). We confirm that the epenthetic stop perceived is the one predicted by articulatory accounts of how such stops are produced, and that the likelihood of an epenthetic stop being perceived as a real stop is related to the strength of acoustic cues in the signal. We show that the probability of listeners mis-parsing epenthetic stops as real is influenced by language-specific syllable structure constraints, and depends on processing demands. We further show, through reaction time data, that even when epenthetic stops are perceived, they impose a greater processing load than stops which were intended by the speaker. These results show that processing of phonetic variability is affected by several factors, including language-specific phonology, even though the mis-timing of articulations that creates epenthetic stops is universally possible.