MPLS tunnels and LSPs

Consider a LSP .  Let us suppose that R1 receives unlabeled packet P,
and pushes on its label stack the label to cause it to follow this path,
and that this is in fact the Hop-by-hop path.

However, let us further suppose that R2 and R3 are not directly connected,
but are "neighbors" by virtue of being the endpoints of an
LSP tunnel.  So the actual sequence of LSRs traversed by P is
.

When P travels from R1 to R2, it will have a label stack of depth 1.

R2, switching on the label, determines that P must enter the tunnel.

R2 first replaces the Incoming label with a label that is meaningfulto R3.
Then it pushes on a new label.  This level 2 label has a
value which is meaningful to R21.
Switching is done on the level 2 label by R21, R22, R23.  R23,
which is the penultimate hop in the R2-R3 tunnel, pops the label stack
before forwarding the packet to R3.

When R3 sees packet P, P has only a level 1 label, having now exited the tunnel.
Since R3 is the penultimate hop in P's level 1
LSP, it pops the label stack, and R4 receives P unlabeled.