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To provide alternative refrigerants for R410A in those applications where the GWP (global warming potential) limit is extremely restrictive in the medium and long term. This work investigated refrigerant blends in both air-conditioning and heat pump applications that can provide similar theoretical cycle performance to R410A. We carried out an extensive screening of blends with a maximum of five components among a list of 12 pure refrigerants comprising three hydrofluoroolefins, five hydrofluorocarbons, two hydrocarbons, CO2 and R13I1. These mixtures were subjected to a multi-parameter optimization process consisting of GWP, flammability and thermodynamic models. The screening metrics included low GWP (≤150), mild flammability, small temperature glide (≤10 K), maximum COP (coefficient of performance) and similar volumetric capacity. In total, 34 mixtures were identified to fulfill all the criteria, all of them presented mild flammability and a GWP value below 150, in which 11 mixtures were less than 10. Most of the selected mixtures operated with temperature glide less than 5 K, the mixtures composed by R32/R1123/R13I1 offered an increment of -4% to 17% for the volumetric capacity, but the COPs decreased slightly from 5–10%. Finally, we found 4 mixtures that had almost the same vapor pressure to that of R410A, they were R32/R1123/R161/R13I1 (20/40/10/30), R1123/R161/R13I1 (65/5/30), R1123/R152a/R13I1 (65/5/30) and R1123/R1234ze(E)/R13I1 (65/5/30). The screening results fulfill all the restrictions for the first time, though a further experimental test is needed to confirm the real applicability.