Perovskite rare-earth cobaltites ACoO3 (A = Sc, Y, La-Lu) have been of enduring interest for decades due to their unusual structural and physical properties associated with the spin-state transitions of low-spin Co3+ ions. Herein, we have synthesized a non-rare-earth perovskite cobaltite, InCoO3, at 15 GPa and 1400 °C and investigated its crystal structure and magnetic ground state. Under the same high-pressure and high-temperature conditions, we also prepared a perovskite-type ScCoO3 with an improved cation stoichiometry in comparison to that in a previous study, where synthesis at 6 GPa and 1297 °C yielded a perovskite cobaltite with cation mixing on the A-site, (Sc0.95Co0.05)CoO3. The two perovskite phases have nearly stoichiometric cation compositions, crystallizing in the orthorhombic Pnma space group. In the present investigation, comprehensive studies on newly developed and well-known Pnma ACoO3 perovskites (A = In, Sc, Y, Pr-Lu) show that InCoO3 does not fulfill the general evolution of crystal metrics with A-site cation size, indicating that InCoO3 and rare-earth counterparts have different chemistry for stabilizing the Pnma structures. Detailed structural analyses combined with first-principles calculations reveal that the origin of the anomaly for InCoO3 is ascribed to the A-site cation displacements that accompany octahedral tilts; despite the highly tilted CoO6 network, the In-O covalency makes In3+ ions reluctant to move from their ideal cubic-symmetry position, leading to less orthorhombic distortion than would be expected from electrostatic/ionic size mismatch effects. Magnetic studies demonstrate that InCoO3 and ScCoO3 are diamagnetic with a low-spin state of Co3+ below 300 K, in contrast to the case of (Sc0.95Co0.05)CoO3, where the high-spin Co3+ ions on the A-site generate a large paramagnetic moment. The present work extends the accessible composition range of the low-spin orthocobaltite series and thus should help to establish a more comprehensive understanding of the structure-property relation.