  We elaborate on the recently proposed static brane world scenario, where the
effective 4-D cosmological constant is exponentially small when parallel
3-branes are far apart. We extend this result to a compactified model with two
positive tension branes. Besides an exponentially small effective 4-D
cosmological constant, this model incorporates a Randall-Sundrum-like solution
to the hierarchy problem. Furthermore, the exponential factors for the
hierarchy problem and the cosmological constant problem obey an inequality that
is satisfied in nature. This inequality implies that the cosmological constant
problem can be explained if the hierarchy problem is understood. The basic idea
generalizes to the multibrane world scenario. We discuss models with piecewise
adjustable bulk cosmological constants (to be determined by the 5-dimensional
Einstein equation), a key element of the scenario. We also discuss the global
structure of this scenario and clarify the physical properties of the particle
(Rindler) horizons that are present. Finally, we derive a 4-D effective theory
in which all observers on all branes not separated by particle horizons measure
the same Newton's constant and 4-D cosmological constant.
