Let DM′cdh(k) be the variant of Voevodsky’s category where the big Nisnevich site Sm/k is replaced by the big cdh site Sch/k. We prove that the canonical functor: DMNis(k)− > DMcdh(k) admits a section. We get in particular the following weak cdh-descent result: Let H.-¿X be a simplicial cdh-hypercover of a smooth k-scheme X. Assume that all the component Hn are smooth over k. Then Ztr(H.)− > Ztr(X) is an A1-weak equivalence.