  We devise a measure n(r) to quantify a robust feature in the coherent cosmic
perturbations, namely the narrowness of the first peak in the power spectrum of
the Cosmic Microwave Background (CMB) anisotropy. A maximum-likelihood analysis
using the WMAP data shows that the power fraction of any defect models at the
first peak is persistently less than 4.5% at the 68% confidence. Our approach
and results are insensitive to the uncertainties in the theoretical predictions
for defect models, and thus the most robust to date. We show that to convert
these results into realistic constraints on theories such as inflation, string
cosmology, and SUSY GUTs, a more robust study for the cosmic-string-induced CMB
around the degree scale is required.
