  We prove distributional limit theorems (conditional and integrated) for the
occupation times of certain weakly mixing, pointwise dual ergodic
transformations at "tied-down" times immediately after "excursions". The
limiting random variables include the local times of $p$-stable L\'evy-bridges
($1<p\le 2$) and the transformations involved exhibit "tied-down renewal
mixing" properties which refine rational weak mixing. Periodic local limit
theorems for Gibbs-Markov and AFU maps are also established.
