Teacher value-added models (VAMs) must isolate teachers' contributions to student achievement to be valid. Well-known VAMs use different specifications, however, leaving policymakers with little clear guidance for constructing a valid model. We examine the sensitivity of teacher value-added estimates under different models based on whether they include student and peer background characteristics, and a double-lagged achievement score. We also consider two previously unexplored model variations: (a) replacing classroom peer characteristics with teacher-level averages, and (b) allowing demographics to influence the relationship between current and prior achievement. Using data from a northern state, we find that teacher effectiveness estimates are highly correlated across specifications. However, up to 26% of teachers in the bottom quintile using one specification are ranked higher using another specification. Differences between VAMs have direct implications for which estimates change. In particular, teachers in a district with a large fraction of disadvantaged students receive lower ratings when background characteristics are omitted. Other modeling choices have smaller practical consequences, and none are as important as selecting which assessment to use as the outcome measure.