  In the spirit of Lehmer's speculation that Ramanujan's tau-function never
vanishes, it is natural to ask whether any given integer $\alpha$ is a value of
$\tau(n)$. For any given odd $\alpha$, Murty, Murty, and Shorey proved that
$\tau(n)\neq \alpha$ for sufficiently large $n$. Several recent papers consider
the case of odd $\alpha.$ In this note, we determine examples of even integers
that are not tau-values. Namely, for the indicated primes $\ell$, we prove that
\[\begin{split}
  \tau(n)\not \in \{ \pm 2\cdot 691\} &
  \cup \{2\ell \ : \ 3\leq \ell \leq 97\ {\text with}\ \ell \neq 43, 79\}\\
&\cup \{-2\ell \ : \ 3\leq \ell \leq 97\ {\text with}\ \ell\neq 5, 17, 41, 47,
59, 89\}
  \cup \{-2\ell^2 \ : \ 3\leq \ell \leq 23\}. \end{split}\] The method of proof
applies mutatis mutandis to newforms with residually reducible mod 2 Galois
representation and is easily adapted to generic newforms with integer
coefficients.
