If a principal G-bundle \(P\to M\) has connection \(\vartheta\) and curvature \(\theta\), \(\vartheta\) is said to be fat at \(\mu\in {\mathfrak g}\) * if the horizontal real-valued form \(\) is non-degenerate on each horizontal subspace of TP. The set S of points at which \(\vartheta\) is fat is an open G-invariant conic set in \({\mathfrak g}\) *. Following Sternberg and Weinstein, the importance of fatness lies in the fact that if \(J: Q\to {\mathfrak g}\) * is the moment map for some Hamiltonian G-space Q, then J(Q)\(\subset S\subset {\mathfrak g}\) * implies that \(P\times_ GQ\) possesses a symplectic structure. The author shows that the standard connection on the principal H-bundle \(K\to K/H\) coming from a coadjoint orbit is always fat away from certain walls of Weyl chambers in \({\mathfrak h}\) *. Then symplectic fibre bundles over K/H may be constructed.