Current methods to extract the quark-mixing matrix element | V tb | from single-top-production measurements assume that | V tb |≫| V td |,| V ts |: top quarks decay into b quarks with 100 % branching fraction, s -channel single-top production is always accompanied by a b quark and initial-state contributions from d and s quarks in the t -channel production of single top quarks are neglected. Triggered by a recent measurement of the ratio performed by the D0 collaboration, we consider a | V tb | extraction method that takes into account non zero d - and s -quark contributions both in production and decay. We propose a strategy that allows to extract consistently and in a model-independent way the quark-mixing matrix elements | V td |, | V ts |, and | V tb | from the measurement of R and from single-top measured event yields. As an illustration, we apply our method to the Tevatron data using a CDF analysis of the measured single-top event yield with two jets in the final state, one of which is identified as a b -quark jet. We constrain the | V tq | matrix elements within a four-generation scenario by combining the results with those obtained from direct measurements in flavor physics and determine the preferred range for the top-quark decay width within different scenarios.