Message Sequence Charts (MSCs) is a visual formalism for the description of communication behaviour of distributed systems. An MSC specifies relations between communication events with partial orders. A situation when two visually ordered events may occur in any order during an execution of an MSC is called a race and is usually considered as a design error. While there is a quadratic time algorithm detecting races in a finite communication behaviours called Basic Message Sequence Charts (BMSCs), the race detection problem is undecidable for High-level Message Sequence Charts (HMSCs), an MSC formalism describing potentially infinite sets of potentially unbounded behaviours. To improve this negative situation for HMSCs, we introduce two new notions: a new concept of race called trace-race and an extension of the HMSC formalism with open coregions, i.e. coregions that can extend over more than one BMSC. We present three arguments showing benefits of our notions over the standard notions of race and HMSC. First, every trace-race-free HMSC is also race-free. Second, every race-free HMSC can be equivalently expressed as a trace-race-free HMSC with open coregions. Last, the trace-race detection problem for HMSC with open coregions is decidable and PSPACE-complete. Finally, the proposed extension of coregions allows to represent in a visual fashion whether an arbitrary number of racing events in the usual MSC formalism are concurrent or not.