Ideals Whose First Two Betti Numbers are Close

For an ideal $I$ of a Noetherian local ring $(R,\text{fm},k)$ we show that ${\text{bt}}_1^R(I)-{\text{bt}}_0^R(I)\ge -1$. It is demonstrated that some residual intersections of an ideal $I$ for which $\bt_1^R(I)-\bt_0^R(I)= -1;$\text{or}$;0$ are perfect. Some relations between Betti numbers and Bass numbers of the canonical module are studied.