The use of recycled aggregates (RAs) for concrete promotes circular construction while the introduction of lateritic soil (LS) seeks cost reduction in concrete production. This study reports the results of experiments on partial replacement of (i) Akure-pit sand (APS) with recycled fine aggregate (RFA); (ii) RFA with LS; (iii) APS with LS; and (iv) crushed granite (CG) with recycled coarse aggregate (RCA). Replacement levels were from 0% to 70% in steps of 10%. Major tests were compressive strength and sorptivity. The performance index approach was employed to obtain the best performance indices for various material combinations. The results revealed that at 28 days of curing, concretes attained optimum compressive strengths of 15 N/mm2, 15.1 N/mm2, 13.1 N/mm2, and 16.8 N/mm2, respectively for mixtures produced by partially substituting APS with 70%RFA; RFA with 40%LS; APS with 50%LS; and CG with 50%RCA. The sorptivity was optimal at 2.69×10-4 mm/min0.5; 3.58×10-4 mm/min0.5; 3.16×10-4 mm/min0.5; and 2.86×10-4 mm/min0.5, respectively for mixtures with partial replacement of APS with 30%RFA; RFA with 40%LS; APS with 40%LS; and CG with 10%RCA. This research will find practical application in construction works utilizing LS and RAs when optimal replacement levels of the conventional aggregates are required, in order to achieve predetermined performance criteria.