One of the challenges that all accelerators face, is to execute loops that have if-then-else constructs. There are three ways to accelerate loops with an if-then-else construct on a Coarse-grained reconfigurable architecture (CGRA): full predication, partial predication, and dual-issue scheme. In comparison with the other schemes, dual-issue scheme may achieve the best performance, but it requires compiler support - which does not exist. In this paper, we develop compiler techniques to map loops with conditionals on CGRA for the dual-issue scheme. Our experiments show: i) 40% of loops that can be accelerated on CGRA have conditionals, ii) The proposed dual-issue scheme enables our compiler to accelerate loops 40% faster than full predication scheme proposed in , and iii) Our compiler assisted dual issue scheme can exploit richer interconnects, if present.