  The Cosmic Microwave Background (CMB) fluctuations at very small angular
scales (less than $10'$) induced by matter sources are computed in a simplified
way. The result corrects a previous formula appearing in the literature. The
small scale power spectrum from cosmic strings is then calculated by a new
analytic method. The result compares extremely well with the spectrum computed
by numerical techniques (when the old, incorrect, formula is used). The upper
bound on the string parameters derived from OVRO data is re-examined, taking
into account the non-Gaussian nature of stringy perturbations on small scales.
Assuming a conventional ionization history, the bound is $\gamma G\mu <
11\times 10^{-6}$, where $\gamma^2$ is the number of horizon lengths of string
per horizon volume. Current simulations give $\gamma^2 = 31\pm 7$.
