A very long-standing problem in Algebraic Geometry is to determine the stability of exceptional bundles on smooth projective varieties. We first show that if $X\subset P^n$, $n\geq 3$, is a smooth and irreducible hypersurface of degree $1\leq d\leq n-1$ and $E$ is an exceptional bundle on $X$ given by \[ 0 \rightarrow \mathcal{O}_{X}(-1)^{r} \rightarrow \mathcal{O}_{X}^{s} \rightarrow E \rightarrow 0, \] for some $s,t\geq 1$, then $E$ is stable. We then prove that any exceptional bundle on a smooth complete intersection $3$-fold $Y\subset P^n$ of type $(d_1,\ldots,d_{n-3})$ with $d_1+\cdots+ d_{n-3}\leq n$ and $n\geq 4$, is stable. (joint work with Rosa M. Miró-Roig)