  Let $(m,b)$ be a pair of natural numbers. For $m$ odd with $m \ge 7$ (resp.
$m \ge 5$) and $b=1$ (resp. $b=0$) we show that there is a non-formal compact
(almost) contact $m$-manifold with first Betti number $b_1 = b$. Moreover, in
the case $b = 0$ with $m \ge 7$, the manifold even is simply-connected.
