We put forward the conjecture that the small numbers in the V_text {CKM} matrix, are generated by physics beyond the Standard Model. We identify as small numbers V_{ub} and the strength of CP violation, measured by |text {Im}Q|, where Q stands for a rephasing invariant quartet of V_text {CKM}. We illustrate how the conjecture can be realised in the context of an extension of the Standard Model where an up-type vector-like quark is introduced leading to a realistic spectrum of quark masses and an effective V_text {CKM} in agreement with experiment.