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Although, as part of a general phenomenon, the piezoelectric response of Ba(Ti1-yMy)O3 (M=Zr, Sn, Hf) increases in the vicinity of the orthorhombic (Amm2)-tetragonal (P4mm) and orthorhombic (Amm2)-rhombohedral (R3m) polymorphic phase boundaries, experiments in the last few years have shown that the same phase boundaries show significantly enhanced weak-field piezoproperties in the Ca-modified variants of these ferroelectric alloys, i.e., (Ba,Ca)(Ti,M)O3. So far there is a lack of clarity with regard to the unique feature(s) which Ca modification brings about that enables this significant enhancement. Here, we examine this issue from a structural standpoint with M=Sn as a case study. We carried out a comprehensive comparative structural, ferroelectric, and piezoelectric analysis of the Amm2 phase in the immediate vicinity of the P4mm-Amm2 phase boundaries of (i) Ca-modified Ba(Ti,Sn)O3, as per the nominal formula (1-x)BaTi0.88Sn0.12O3-(x)Ba0.7Ca0.3TiO3 and (ii) without Ca modification, i.e., Ba(Ti1-ySny)O3. We found that the spontaneous lattice strain of the Amm2 phase is noticeably smaller in the Ca-modified counterpart. Interestingly, this happens along with an improved spontaneous polarization by enhancing the covalent character of the Ti-O bond. Our study suggests that the unique role of Ca modification lies in its ability to induce these seemingly contrasting features (reduction in spontaneous lattice strain but increase in polarization). [ABSTRACT FROM AUTHOR]