Linear asymmetries pose a challenge for syntactic theory but may yield to an explanation in terms of sentence parsing, given the inherent left-to-right nature of this process. We therefore explore the option of a parsing-based account of Greenberg’s (1963) universal 20. Universal 20 describes a word-order asymmetry in noun phrases that can be captured if movement of the noun is exclusively leftward (Cinque 2005 and Abels & Neeleman 2012). Our account is based on the hypothesis that rightward movement of obligatory elements leads to a specific processing difficulty that we call the missing-filler effect. Independent evidence for this effect comes from self-paced reading and maze paradigm experiments that replicate and extend earlier findings by Staub et al. (2006) regarding the parsing of heavy-XP shift in the context of optionally and obligatorily transitive verbs. We conclude that the absence of rightward movement in the noun phrase need not be attributed to a syntactic constraint but can be traced back to the missing-filler effect if we assume that parsing effort affects language acquisition, which in turn affects typological frequency (as argued in Hawkins 1990, 2009 and Kirby 1999).