Many studies of human sequential pattern learning demonstrate that learners detect adjacent and non-adjacent dependencies in many kinds of sequences. However, it is often assumed that the computational mechanisms behind extracting these dependencies are the same. We replicate the seminal finding that adults are capable of learning dependencies between non-adjacent words (Gómez, 2002). When we eliminate the positional information about the statistical structures by embedding the structure in phrases, learners can no longer learn the dependencies. Our methods allow us to study the learning mechanisms that are more representative of the patterns in natural languages, and show that when directly compared, adjacent and non-adjacent dependencies are not equally learnable. We suggest that learning non-adjacent dependencies in language involves a different computational mechanism from learning adjacent dependencies.