There are many examples of fluid motions that give kinematic dynamos in an infinite medium, but very few cases of dynamos in an electrical conductor of bounded extent. This curious observation is investigated by numerical calculation. Two significant effects are revealed. An insulating boundary is found to cause a current sheet to form near it and this inhibits magnetic field generation. Also the ratio of poloidal to toroidal component of fluid flow must lie in a certain range for dynamo action to occur, because otherwise the diffusive effects of the separate components dominate the regeneration mechanism which requires a combination of both. These two effects help account for some of the difficulties encountered in constructing kinematic dynamo models, and are relevant to the problem of generation of magnetic field by thermal convection in a rotating system.