In the [Fe(ptz)₆](BF₄)₂ (ptz = 1-propyltetrazole) spin-crossover system, the thermal spin transition is accompanied by a first order crystallographic phase transition (T_c^↓ = 128 K and T_c^↑ = 135 K) from R³ above T_c^↓ to P¹ at low temperatures (Wiehl L., Acta Cryst. B49, 289 (1993)). The high-symmetry phase can be super-cooled, in which case the spin transition is still complete and quite steep (T_1/2 = 125 ± 2 K) but now without a hysteresis. The corresponding interaction constant Γ is 170 cm⁻¹. In the diluted system [Zn_1−xFe_x(ptz)₆](BF₄)₂, X = 0.1, the spin transition is gradual with T_1/2 = 95 ± 2 K. From the shift of T_1/2 towards high temperatures with external pressure a value for ΔV_HL⁰ of 26 ų molecule⁻¹ is obtained. Pressures above 250 bar induce a crystallographic phase transition even in the diluted system, as a result of which the spin transition is discontinuous. The interplay between the thermal spin transition and the crystallographic phase transition in the neat and the diluted system is discussed consistently.