The computational identification of RNAs in genomic sequences requires the identification of signals of RNA sequences. Shannon base pairing entropy is an indicator for RNA secondary structure folding certainty, in the detection of structural non-coding RNAs (ncRNAs). Under the Boltzmann ensemble of secondary structures, the probability of a base pair is estimated from its frequency across all the alternative equilibrium structures. However, such an entropy has yet to deliver the desired performance distinguishing ncRNAs from random sequences. Developing novel methods to improve the entropy measure performance may result in more effective ncRNA gene finding based on structure detection. This paper shows that the measuring performance of base pair entropy can be significantly improved with a constrained secondary structure ensemble in which only canonical base pairs are assumed to occur, and energetically stable stems are required, in a fold. This constraint actually reduces the space of the secondary structure and may lower probabilities of base pairs unfavorable to the native fold. Indeed, base pair entropies computed with this constrained model demonstrate substantially narrowed gaps of Z-scores between ncRNAs as well as drastic increases in the Z-score for all 13 tested ncRNA sets compared to shuffled sequences.