In multiattribute inferences, cross-validation studies of out-of-sample accuracy have shown that fast and frugal heuristics such as take-the-best often outperform weighted additive models such as Multiple Regression, Naïve Bayes and Tally (Brigthon & Gigerenzer, 2009). From a prescriptive perspective, the results imply that decision accuracy may actually decrease when attributes are searched beyond the most valid and discriminating. Lee and Zhang (2012) showed that especially in redundant (positively correlated) environments, the evidence gained from an exhaustive search of all attributes will frequently predict the same option as the evidence gained from the frugal search of the most valid discriminating attribute. In the present study, we assessed how (1) simple and cognitively plausible limitations of information search (2 to 6 most valid attributes), and, (2) attribute redundancy, affect the relative out-of-sample performance of strategies. The strategies were cross-validated on 15 real-world data sets studied previously, and on simulated multivariate normal data with redundancy manipulated via the covariance matrix. Our results show that under high redundancy, Naïve Bayes and Tally with limited search show similar accuracy as take-the-best, whereas the letter perform relatively worse under low redundancy. We discuss the prescriptive implications for information search, search termination and information combination in multiattribute inferences.