  Let $SV^{\pmb n}_{\pmb d}$ be the Segre-Veronese given as the image of the
embedding induced by the line bundle
$\mathcal{O}_{\mathbb{P}^{n_1}\times\dots\times\mathbb{P}^{n_r}}(d_1,\dots,
d_r)$. We prove that asymptotically $SV^{\pmb n}_{\pmb d}$ is not $h$-defective
for $h\leq n_1^{\lfloor \log_2(d-1)\rfloor}$.
