Without demanding that the functions f(q2) and g(q2) in the structure function xF3(x,q2)=Cx1mf/(1-x)ng be slowly varying, upper and lower bounds are obtained for the slope of the graph for 1g MN against 1g MN', where MN is the Nth moment of xF3(x,q2). The bounds obtained here also include the predictions of scalar gluon theories which is not the case for Harari's bounds (1979). Further, it is observed that the bounds are sensitive to the way in which the q2 dependence is introduced in xF3(x,q2).