In this paper we discuss two distinct, although related questions. The first question is what explains the well-known fact that short-term memory (span) is lower for signs than for words. We review some explanations that have been proposed for this fact at the light of the results of a novel experiment involving gating of signs. The second question is how signers can process fully-fledged grammatical systems like sign languages even if they rely on a limited short-term memory. In order to deal with this issue, we discuss the distribution in sign languages of the configuration that is most challenging for short-term memory, namely center embedding. The conclusion is that center embedding is possible only if special strategies based on the use of space are used that are likely to reduce the short-term memory burden.