  "Brane Induced Gravity" is regarded as a promising framework for addressing
the cosmological constant problem, but it also suffers from a ghost instability
for parameter values that make it phenomenologically viable. We carry out a
detailed analysis of codimension > 2 models employing gauge invariant variables
in a flat background approximation. It is argued that using instead a curved
background sourced by the brane would not resolve the ghost issue, unless a
very specific condition is satisfied (if satisfiable at all). As for other
properties of the model, from an explicit analysis of the 4-dimensional
graviton propagator we extract a mass, a decay width and a momentum dependent
modification of the gravitational coupling for the spin 2 mode. In the flat
space approximation, the mass of the problematic spin 0 ghost is instrumental
in filtering out a brane cosmological constant. The mass replaces a background
curvature that would have had the same function. The optical theorem is used to
demonstrate the suppression of graviton leakage into the uncompactified bulk.
Then, we derive the 4-dimensional effective action for gravity and show that
general covariance is spontaneously broken by the bulk-brane setup. This
provides a natural realization of the gravitational Higgs mechanism. We also
show that the addition of extrinsic curvature dependent terms has no bearing on
linearized brane gravity.
