  In quantum gravity it is generally thought that a modified commutator of the
form $[{\hat x}, {\hat p}] = i \hbar (1 + \beta p^2)$ is sufficient to give
rise to a minimum length scale. We test this assumption and find that different
pairs of modified operators can lead to the same modified commutator and yet
give different or even no minimal length. The conclusion is that the
modification of the operators is the main factor in determining whether there
is a minimal length. This fact - that it is the specific form of the modified
operators which determine the existence or not of a minimal length scale - can
be used to keep or reject specific modifications of the position and momentum
operators in theory of quantum gravity.
