The mean squared radius of gyration S-2 of a Short Rouse model polymer composed of N (less than or equal to 50) monomers is determined as a function of the number M (less than or equal to 25) of imposed contacts. The contacts are modelled by extra harmonic potentials between the specified monomers. A Green’s function method is used to follow the effects of sequential addition of contacts. Averaging over random sequences of contacts leads to the estimate [S-2](M)=[S-2](0)/(1+0.43M).