  We study $M$-ideals of compact operators by means of the property~$(M)$
introduced in \cite{Kal-M}. Our main result states for a separable Banach space
$X$ that the space of compact operators on $X$ is an $M$-ideal in the space of
bounded operators if (and only if) $X$ does not contain a copy of $\ell_{1}$,
has the metric compact approximation property, and has property~$(M)$. The
investigation of special versions of property~$(M)$ leads to results on almost
isometric structure of some classes of Banach spaces. For instance, we give a
simple necessary and sufficient condition for a Banach space to embed almost
isometrically into an $\ell_{p}$-sum of finite-dimensional spaces resp.\ into
$c_{0}$, and for $2<p<\iy$ we prove that a subspace of $L_{p}$ embeds almost
isometrically into $\ell_{p}$ if and only if it does not contain a subspace
isomorphic to $\ell_{2}$.
