I propose a model in which agents decide on job search intensity for each possible wage, unlike the usual setup of constant search intensity over wage draws. The proposed framework entails efficiency gains in that agents do not waste effort to searching for low paying unacceptable jobs or less offered high paying jobs. The proposed framework generates accepted wages distributions that differ substantially from the truncated distributions stemming from the usual setup. These different empirical implications are exploited for building two nonparametric tests, which reject constant search intensity over wages, using NLSY97 data. I further estimate the identifiable structural parameters of the two models resulting in better fit for the wage-specific setup. I quantify the increased effectiveness of wage-specific search in more total search intensity, faster transitions to the upper tail of the wage distribution, and higher wages, in particular, more than 25% increase in accepted wages after unemployment.