Abstract
A direct and elementary scheme for the construction of Miura-type transformations and discrete differential equations related to them (scalar and vector) is presented. The scheme is illustrated using as examples the Volterra and Toda models. A discrete-differential analogue of the Calogero-Degasperis equation is discussed in detail. This example is used to show how to construct conservation laws, higher symmetries, and solutions for an equation obtained with the help of the scheme.