We propose a new definition of the class of search problems that correspond to \(\mathcal{BPP}\) . Specifically, a problem in this class is specified by a polynomial-time approximable function \(q:\{0,1\}^*\times \{0,1\}^*\rightarrow [0,1]\) that associates, with each possible solution y to an instance x, a quality q(x, y). Intuitively, quality 1 corresponds to perfectly valid solutions, quality 0 corresponds to perfectly invalid solutions, but the quality of other solutions can be anywhere in-between. The class of PPT-search problems contains q if there exists a PPT algorithm that, on input x, finds a solution with value close to \(\max _y\{q(x,y)\}\) . We relate this definition to previously studied definitions of “BPP-search problems” and articulate our preference for it. More importantly, we show that any PPT-search problem can be reduced in deterministic polynomial-time to a promise problem in \({\textrm{pr}{\mathcal{BPP}}}\) (i.e., promise-BPP).