  Let $V$ be a finite relational vocabulary in which no symbol has arity
greater than 2. Let $M$ be countable $V$-structure which is homogeneous, simple
and 1-based. The first main result says that if $M$ is, in addition, primitive,
then it is strongly interpretable in a random structure. The second main
result, which generalizes the first, implies (without the assumption on
primitivity) that if $M$ is "coordinatized" by a set with SU-rank 1 and there
is no definable (without parameters) nontrivial equivalence relation on $M$
with only finite classes, then $M$ is strongly interpretable in a random
structure.
