Gaussian statistics of random walks and/or "ideal" polymers is heavily dependent on the presence of configurations with knots. If knots are excluded by, e.g., loop preparation, then such loop is not Gaussian. Extensive simulation confirms earlier predictions that no-knots loop has the statistics similar to that of a self-avoiding walk, even if real excluded volume is completely negligible. Thus, global topological constraint leads to local polymer swelling for a free loop. By contrast, compact polymer loop constrained to have no knots and to occupy minimal possible volume exhibits opposite effect, with every piece of a polymer somewhat shrunken.