We examine the "puffed-up inner disk" model (Dullemond, Dominik & Natta 2001), proposed for explaining the near-IR excess radiation from Herbig Ae/Be stars. Detailed model computations show that the observed near-IR excess requires more hot dust than is contained in the puffed-up disk rim. The rim can produce the observed near-IR excess only if its dust has perfectly gray opacity, but such dust is in conflict with the observed 10μm spectral feature. We find that a compact (∼ 10 AU) tenuous (τ_V

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... 0.4) dusty halo around the disk inner regions contains enough dust to readily explain the observations. Furthermore, this model also resolves the puzzling relationship noted by Monnier and Millan-Gabet (2002) between luminosity and the interferometric inner radii of disks.