A bicycle rear shock absorber, comprising: a damper tube having a first end portion, a second end portion and a side wall extending between said first end portion and said second end portion; a piston rod that carries a first piston, said first piston and said piston rod capable of telescopic movement with respect to said damper tube, wherein said first piston cooperates with said damper tube to at least partially define a variable volume compression chamber and said piston rod extends out of said first end portion of said damper tube; a seal head that creates a seal between said first end portion of said damper tube and said piston rod; a remote reservoir tube having a first end portion, a second end portion and a side wall extending between said first end portion and said second end portion, wherein said remote reservoir tube and said damper tube are not within one another, wherein at least a portion of said remote reservoir tube defines a reservoir chamber; a fluid passage that extends between said compression chamber and said reservoir chamber, wherein said damper tube defines a first opening that permits fluid communication between said compression chamber and said fluid passage, and said remote reservoir tube defines a second opening that permits fluid communication between said fluid passage and said reservoir chamber; a compression damping circuit within said remote reservoir tube that regulates compression fluid flow between said compression chamber and said reservoir chamber, said compression damping circuit comprising a pressure-activated valve and an acceleration-activated valve, said pressure-activated valve includes a partition defining more than one axial compression flow passage and one or more refill ports, said acceleration-activated valve including an inertia mass, characterized in that said partition is upstream from said inertia mass relative to a flow of compression fluid from said second opening to said reservoir chamber, and wherein the compression damping circuit is configured such that a flow of fluid within said reservoir chamber tends to pass alongside the inertia mass and assist in opening the inertia mass during compression motion of the shock absorber, and tends to pass alongside the inertia mass and assist in closing the inertia mass during rebound motion of the shock absorber. a damper tube having a first end portion, a second end portion and a side wall extending between said first end portion and said second end portion; a piston rod that carries a first piston, said first piston and said piston rod capable of telescopic movement with respect to said damper tube, wherein said first piston cooperates with said damper tube to at least partially define a variable volume compression chamber and said piston rod extends out of said first end portion of said damper tube; a seal head that creates a seal between said first end portion of said damper tube and said piston rod; a remote reservoir tube having a first end portion, a second end portion and a side wall extending between said first end portion and said second end portion, wherein said remote reservoir tube and said damper tube are not within one another, wherein at least a portion of said remote reservoir tube defines a reservoir chamber; a fluid passage that extends between said compression chamber and said reservoir chamber, wherein said damper tube defines a first opening that permits fluid communication between said compression chamber and said fluid passage, and said remote reservoir tube defines a second opening that permits fluid communication between said fluid passage and said reservoir chamber; a compression damping circuit within said remote reservoir tube that regulates compression fluid flow between said compression chamber and said reservoir chamber, said compression damping circuit comprising a pressure-activated valve and an acceleration-activated valve, said pressure-activated valve includes a partition defining more than one axial compression flow passage and one or more refill ports, said acceleration-activated valve including an inertia mass, characterized in that said partition is upstream from said inertia mass relative to a flow of compression fluid from said second opening to said reservoir chamber, and wherein the compression damping circuit is configured such that a flow of fluid within said reservoir chamber tends to pass alongside the inertia mass and assist in opening the inertia mass during compression motion of the shock absorber, and tends to pass alongside the inertia mass and assist in closing the inertia mass during rebound motion of the shock absorber.