  We establish an $h$-principle for exact Lagrangian immersions with transverse
self-intersections and the minimal, or near-minimal number of double points.
One corollary of our result is that any orientable closed 3-manifold admits an
exact Lagrangian immersion into standard symplectic 6-space $\R^6_\st$ with
exactly one transverse double point. Our construction also yields a Lagrangian
embedding $S^1\times S^2\to\R^6_\st$ with vanishing Maslov class.
