  We prove a version of the Beurling-Malliavin multiplier theorem. This version
is formulated here in a simplified form. Let $u\not\equiv -\infty$ and
$M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane
$\mathbb C$ with positive parts $u^+:=\sup\{u,0\}$ and $M^+$ such that $$
\operatorname{type}[u]:=\limsup_{z\to \infty} \frac{u^+(z)}{|z|}<+\infty,
\qquad \operatorname{type}[M]<+\infty, \qquad
\int_{-\infty}^{+\infty}\frac{u^+(x)+M^+(x)}{1+x^2}\operatorname{d}x<+\infty.
$$ If $\operatorname{type}[u]<a<+\infty$, $0<b<+\infty$, and
$\operatorname{type}[M]<c<+\infty$, then there are an entire function
$h\not\equiv 0$ with $\operatorname{type}[\log|h|]<c$ and a subset $iY$ in the
imaginary axis $i\mathbb R$ of linear Lebesgue measure $<b$ such that the
function $h$ is bounded on the real axis and $u(z)-M(z)+\log|h(z)|\leq a|\Im
z|$ on each straight line parallel to the real axis and not intersecting $iY$.
