  In this paper we investigate the behavior of the bridges of a Markov counting
process in several directions. We first characterize convexity(concavity) in
time of the mean value in terms of lower (upper) bounds on the so called
\textit{reciprocal characteristics}. This result gives a natural criterion to
determine whether bridges are "lazy" or "hurried". Under the hypothesis of
global bounds on the reciprocal characteristics we prove sharp estimates for
the marginal distributions and a comparison theorem for the jump times. When
the height of the bridge tends to infinity we show the convergence to a
deterministic curve, after a proper rescaling.
