  We prove that every (6k + 2l, 2k)-connected simple graph contains k rigid and
l connected edge-disjoint spanning subgraphs. This implies a theorem of Jackson
and Jord\'an [4] and a theorem of Jord\'an [6] on packing of rigid spanning
subgraphs. Both these results are generalizations of the classical result of
Lov\'asz and Yemini [9] saying that every 6-connected graph is rigid for which
our approach provides a transparent proof. Our result also gives two improved
upper bounds on the connectivity of graphs that have interesting properties:
(1) every 8-connected graph packs a spanning tree and a 2-connected spanning
subgraph; (2) every 14-connected graph has a 2-connected orientation.
