In this paper, we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce notion strong partially Markushevich bases and parameters associated with them. prove that property is equivalent to being conservative quasi-greedy, extending a similar result given in Dilworth et al. (Constr Approx 19:575–597, 2003) Schauder bases. also give characterization 1-strong partial...