Reduction theorems for triples of short root unipotent subgroups in Chevalley groups of type B_ℓ and C_ℓ are proved. The main result asserts that except for one case, any subgroup generated by such a triple is conjugate to a subgroup of G(B₄, K)U(B₅, K) or G(C₄, K)U(C₅, K), respectively.