Summary: We study properties of generalized convex hulls of the set \(K=SO(3)\cup SO(3)H\) with \(\det H>0\). If \(K\) contains no rank-1 connection, we show that the quasiconvex hull of \(K\) is trivial if \(H\) belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of \(K\) can be nontrivial if \(H\) is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point, then we demonstrate that the polyconvex hull is trivial provided that there are no rank-1 connections.