One of the difficulties in using the available homotopies to solve sets of algebraic nonlinear equations is the unboundness of the continuation path. This is particularly important when physical properties must be calculated within some prescribed domain. We propose in this paper new homotopies (based on standard ones) with the property of having a continuation path restricted to a prescribed domain. We show with some numerical examples how the proposed homotopies can help to overcome the problem of complex paths. We also show how efficiency can be improved by the use of the proposed homotopies. Scale invariance under diagonal matrices for the variables is also shown.