One feature of Spanish that presents some difficulties to second language (L2) learners whose first language (L1) is English concerns lexical stress. This study explores one aspect of the obstacle these learners face, weak phonological processing routines concerning stress inherited from their native language. Participants were L1 English L2 learners of Spanish. The experiment was a sequence-recall task with auditory stimuli minimally contrasting in stress (target) or segmental composition (baseline). The results suggest that learners are more likely to accurately recall sequences with stimuli contrasting in segmental composition than stress, suggesting reduced phonological processing of stress relative to a processing baseline. Furthermore, an increase in proficiency--assessed by means of grammatical and lexical tests--was found to be modestly associated with an increase in the accuracy of processing stress. We conclude that the processing routines of native English speakers lead to an acquisitional obstacle when learning Spanish as a L2.