  In this letter a new class of twisted strings is presented, with an asymmetry
between the holomorphic and antiholomorphic sectors parametrized by an integer
$N$. Their physical content is given by the massless resonances of the closed
string plus the mass-level $N$ spectrum of the open string. The appeal of this
model is the singling out of the (higher spin) massive levels of string theory
together with their self/gauge/gravity interactions. Motivated by the original
tree level Kawai-Lewellen-Tye relation for closed strings, its asymmetrically
twisted version at four points is conjectured and shown to naturally
interpolate with conventional and twisted strings. The resulting four-point
amplitudes have a generalized Virasoro-Shapiro dressing factor.
