The effects of chain volume and connectivity upon the motions of flexible polymers in dilute solution have been studied by computer simulation of simple off-lattice bead-flip models of from 9 to 99 beads. Long internal relaxation times are given for free-draining chains with bead diameters from zero to 0.93 times the stick lengths. Moves are forbidden which would result either in bead overlap (excluded volume) or in one stick passing through another (chain connectivity). In the extreme case of zero bead diameter, where there is no expansion of the chains by excluded volume, the long relaxation time varies as about the 2.1 power of chain length, as opposed to the 2.0 power for similar chains without connectivity constraints. As bead diameter is increased until it equals stick length, the exponent increases to the value of 2.48 established by previous work. Over the range of bead diameters employed, the chain-length dependence of long relaxation times and translational diffusion constants can be described by the sum of two terms, the first due to chain swelling by excluded volume and consistent with the predictions of scaling theory, the second due only to chain connectivity.