This paper discusses gaps in stress typology that are unexpected from the perspective of a foot-based theory and shows that the patterns pose difficulties for a computationally implemented learning algorithm. The unattested patterns result from combining theoretical elements whose effects are generally well-attested, including iambic footing, nonfinality, word edge alignment and a foot binarity requirement. The patterns can be found amongst the 124 target stress systems constructed by Tesar and Smolensky (2000) as a test of their approach to hidden structure learning. A learner with a Maximum Entropy grammar that uses a form of Expectation Maximization to deal with hidden structure was found to often fail on these unattested languages