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

Constructing exact Lagrangian immersions with few double points