This article considers single replicate factorial experiments in incomplete blocks. A single replicate 2^m1 x 3^m2 deletion design in 3 incomplete blocks is obtained from a single replicate 3^m, where m = m_1 + m_2, preliminary design by deleting all runs (or treatment combinations) with the first m_1 factors at the level two. A systematic method for determining the unbiasedly estimable (u.e.) and not unbiasedly estimable (n.u.e.) factorial effects is provided. It is shown that for m_2 > 0 all factorial effects of the type F( α_1 · · · α_m_1 , α_(m_1 +1) · · · α_m), where α_i; = 0, l for i = 1, · · ·, m_1, α_i; = 0, 1, 2 for i = m_(1+1), · · ·, m, with (α_1 · · · α_m) != (0 · · · 0), and (α_m,+l · · · _m) != α(l · · · 1) for a= 1, 2, are u.e. and the remaining factorial effects are n.u.e. It is noted that (2^m_1 - 1) factorial effects of 2^m_1 factorial experiments and (3^m_2) factorial effects of 3^m, factorial experiments, which are embedded in 2^m_1 x 3^m, factorial experiments, are u. e. The 2 x 3m-l deletion designs were considered in the work of Voss (1986). Defining factorial effects of a 2^m_1 x 3^m, factorial experiment in a form different than in Voss (1986), we develop a simple representation of u.e. and n. u. e. factorial effects. In this representation, there are (2^(m_1 + 1) + 1) n. u. e. factorial effects of the type F( α_1 · · · α_m_1, α· · · α). This number is smaller than the corresponding number of n. u. e. factorial effects in the representation of Voss (1986). The relative efficiency expressions, and their bounds, in the estimation of factorial effects of 2^m_1 x 3^m_2 deletion designs are also given
