  We revisit the problem of determining the independent domination number in
hypercubes for which the known upper bound is still not tight for general
dimensions. We present here a constructive method to build an independent
dominating set $S_n$ for the $n$-dimensional hypercube $Q_n$, where $n=2p+1$,
$p$ being a positive integer $\ge 1$, provided an independent dominating set
$S_p$ for the $p$-dimensional hypercube $Q_p$, is known. The procedure also
computes the minimum independent dominating set for all $n=2^k-1$, $k>1$.
Finally, we establish that the independent domination number $\alpha_n\leq 3
\times 2^{n-k-2}$ for $7\times 2^{k-2}-1\leq n<2^{k+1}-1$, $k>1$. This is an
improved upper bound for this range as compared to earlier work.
