Latin trades are closely related to the problem of critical sets in Latin squares. We denote the cardinality of the smallest critical set in any Latin square of order n by scs(n). A consideration of Latin trades which consist of just two columns, two rows, or two elements establishes that scs(n)greater-or-equal, slantedn-1. We conjecture that a consideration of Latin trades on four rows may establish that scs(n) ≥ 2n-4. We look at various attempts to prove a conjecture of Cavenagh about such trades. The conjecture is proven computationally for values of n less than or equal to 9. In particular, we look at Latin squares based on the group table of View the MathML source for small n and trades in three consecutive rows of such Latin squares.