Substantial transverse Peltier cooling has been reported for synthetic composites consisting of layers of bismuth telluride and either bismuth or lead. Ideally, the two materials in such a composite should have very different values for the electrical and thermal conductivities. If this condition is satisfied, the transverse figure of merit, Zϕ, for the optimum orientation is not much smaller than the longitudinal figure of merit, Z, for the two materials when used as a conventional thermocouple. A second condition is that Z should be as large as possible. We have shown that the two conditions can be met simultaneously if one of the components is porous or otherwise discontinuous. Thus, a highly efficient transverse thermoelement could be made from porous p-type and dense n-type bismuth telluride. Effective transverse thermoelements could also be made from less porous p-type bismuth telluride in conjunction with either single crystal bismuth or YbAl2.96Mn0.04. It is shown that a dimensionless transverse figure of merit, ZϕT, in excess of 0.6 should easily be obtained with these configurations. It should be possible to observe temperature depressions in excess of 100° by the use of suitably shaped synthetic transverse thermoelements.