We present new constructions of (approximate) H(div, Ω)-liftings of the algebraic residual leading to estimators of the algebraic error in h and p finite element discretizations of a model diffusion problem. The estimators provide guaranteed bounds without any uncomputable constants and they are globally efficient, similarly to some recent developments, but the cost of their construction is significantly reduced. We provide a set of numerical experiments to assess the performance of the new estimators.