  Binary $t$-frameproof codes ($t$-FPCs) are used in multimedia fingerprinting
schemes where the identification of authorized users taking part in the
averaging collusion attack is required. In this paper, a binary strongly
$\bar{t}$-separable code ($\bar{t}$-SSC) is introduced to improve such a scheme
based on a binary $t$-FPC. A binary $\bar{t}$-SSC has the same traceability as
a binary $t$-FPC but has more codewords than a binary $t$-FPC. A composition
construction for binary $\bar{t}$-SSCs from $q$-ary $\bar{t}$-SSCs is
described, which stimulates the research on $q$-ary $\bar{t}$-SSCs with short
length. Several infinite series of optimal $q$-ary $\bar{2}$-SSCs of length $2$
are derived from the fact that a $q$-ary $\bar{2}$-SSC of length $2$ is
equivalent to a $q$-ary $\bar{2}$-separable code of length $2$. Combinatorial
properties of $q$-ary $\bar{2}$-SSCs of length $3$ are investigated, and a
construction for $q$-ary $\bar{2}$-SSCs of length $3$ is provided. These
$\bar{2}$-SSCs of length $3$ have more than $12.5\%$ codewords than $2$-FPCs of
length $3$ could have.
