Time Petri Nets (TPN) [Mer74] and Timed Petri Nets [Wal83] are two incomparable classes of concurrent models with timing constraints: urgency cannot be expressed using Timed Petri Nets, while TPNs can only keep track of a bounded number of continuous values ("clocks"). We introduce Timed Petri Nets with Urgency, extending Timed Petri Nets with the main features of TPNs. We present upto-our-knowledge the first decidability results for Petri Net vari-ants combining time, urgency and unbounded places. First, we obtain decidability of control-state reachability for the subclass of Timed Petri Nets with Urgency where urgency constraints can only be used on bounded places. By restricting this class to use a finite number of "clocks", we further show decidability of (marking) reachability. Formally, this class corresponds to TPNs under a new, yet natural, timed semantics where urgency constraints are restricted to bounded places. Fur-ther, under their original semantics, we obtain the decidability of reachability for a more restricted class of TPNs. TPNs