Necessary and sufficient conditions are given for an infinite matrix to sum all bounded strongly summable sequences. It is shown that the Borel matrix does not sum all such sequences. A corollary is that the bounded summability field of the Borel method is strictly contained in that of the $(C,1)$ method. Also, it is proved that no coregular matrix can almost sum all bounded sequencesâa generalization of Steinhausâ theorem.