We examine the constraints that future lepton colliders would impose on the effective field theory describing modifications of top-quark interactions beyond the standard model, through measurements of the $e^+e^-\to bW^+\:bW^-$ process. Statistically optimal observables are exploited to constrain simultaneously and efficiently all relevant operators. Their constraining power is sufficient for quadratic effective-field-theory contributions to have negligible impact on limits which are therefore basis independent. This is contrasted with the measurements of cross sections and forward-backward asymmetries. An overall measure of constraints strength, the global determinant parameter, is used to determine which run parameters impose the strongest restriction on the multidimensional effective-field-theory parameter space.