A product ∏ X i \prod {X_i} of topological spaces X i , i ∈ I {X_i},i \in I will be said to preserve tightness if \[ ∂ ( ∏ X i ) ≤ | I | ⋅ sup { ∂ ( X i ) | i ∈ I } \partial \left ( {\prod {X_i}} \right ) \leq \left | I \right | \cdot {\text {sup}}\left \{ {\partial \left ( {{X_i}} \right )\left | {i \in I} \right .} \right \} \] where ∂ ( X ) \partial \left ( X \right ) denotes the tightness of X X . We show ∏ X i \prod {X_i} preserves tightness whenever each finite subproduct does. It is further shown that this is the case whenever each X i {X_i} is a locally compact T 2 {T_2} -space, and whenever each X i {X_i} is a locally Lindelöf T 3 {T_3} P P -space, extending 5.9 in [J].