  We consider natural variants of Lehmer's unresolved conjecture that
Ramanujan's tau-function never vanishes. Namely, for $n>1$ we prove that
$$\tau(n)\not \in \{\pm 1, \pm 3, \pm 5, \pm 7, \pm 691\}.$$ This result is an
example of general theorems for newforms with trivial mod 2 residual Galois
representation, which will appear in forthcoming work of the authors with
Wei-Lun Tsai. Ramanujan's well-known congruences for $\tau(n)$ allow for the
simplified proof in these special cases. We make use of the theory of Lucas
sequences, the Chabauty-Coleman method for hyperelliptic curves, and facts
about certain Thue equations.
