Icelandic encodes the difference between weak and strong readings of indefinites in terms of (non-)application of object-shift. Tagalog encodes the difference between indefinite and definite themes in terms of "ng-" vs. "ang-"marking. These facts can be taken to observe the principle of "Unambiguous Encoding" (UE), arguably a grammar-internal variant of Gricean "Avoid Ambiguity." However, UE holds in the unmarked case only. Syntactic principles that block object- shift lead to a weak/strong ambiguity of in situ indefinites. Likewise, agent-relativization in Tagalog blocks "ang-"marking of themes, which results in an indefinite/definite ambiguity of "ng-"marked themes. It will be argued that introducing UE as an explicit rankable constraint into standard OT handles these cases in a general way. This suggests that UE may be another instance of the "emergence of the unmarked." At the same time, it seems that bidirectional OT although conceptually superior in deriving effects like "Avoid Ambiguity" from the competition model, fails to predict the Icelandic/Tagalog facts. The remainder of the talk will be devoted to discussing objections to the UE-approach and possible ways out for bidirectionality.