  Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a
nondecreasing sequence of pseudometrics $\{\nu_n\}$ on $M^T$ (the set of all
functions from $T$ into $M$), called the \emph{joint modulus of variation}. We
prove that if two sequences of functions $\{f_j\}$ and $\{g_j\}$ from $M^T$ are
such that $\{f_j\}$ is pointwise precompact, $\{g_j\}$ is pointwise convergent,
and the limit superior of $\nu_n(f_j,g_j)$ as $j\to\infty$ is $o(n)$ as
$n\to\infty$, then $\{f_j\}$ admits a pointwise convergent subsequence whose
limit is a conditionally regulated function. We illustrate the sharpness of
this result by examples (in particular, the assumption on the $\limsup$ is
necessary for uniformly convergent sequences $\{f_j\}$ and $\{g_j\}$, and
`almost necessary' when they converge pointwise) and show that most of the
known Helly-type pointwise selection theorems are its particular cases.
