Multiple recycle of transuranic (TRU) isotopes in thermal reactors results in degradation of the plutonium (Pu) fissile quality with buildup of higher actinides (e.g., Am, Cm, Cf), some of which are thermal absorbers. These phenomena lead to increasing amounts of Pu feed being required to sustain criticality and accordingly larger TRU content in the multirecycled fuel inventory, ultimately resulting in a positive moderator temperature coefficient (MTC) and void reactivity coefficient. Because of the favorable impact fostered by use of thorium (Th) on these coefficients, the feasibility of Th-TRU multiple recycle in reduced-moderation pressurized water reactors (PWRs) and boiling water reactors (BWRs) has been investigated. In this paper, Part I of two companion papers, the analysis is limited to a single assembly, with full-core models presented in Part II. Spatial separation of TRU from bred uranium is found to greatly improve neutronic performance. A large reduction in moderation is necessary to allow full actinide recycle. This will pose thermal-hydraulic challenges, which are discussed in Part II. In addition, the harder neutron spectrum resulting from the reduced moderation also reduces the control rod worth, while there is a neutronic incentive to use increased mechanical shim to maintain a negative MTC. It may therefore be desirable to increase the number of rod cluster control assemblies. Superior burnup is achievable in a reduced-moderation BWR as a larger reduction in moderation is feasible, although the incineration rate is reduced relative to a PWR due to a higher conversion ratio.