diff --git a/HISTORY.md b/HISTORY.md
index d5ca93c..318419c 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -5,9 +5,9 @@ History of SixtyPical
 ----
 
 *   The reference implementation constructs a callgraph and
-    approximates the set of routines which are not called
-    by any other routine, with an eye to omitting them from
-    the final executable.
+    determines the set of routines which are not reachable
+    (directly or indirectly) from `main`, with an eye to
+    omitting them from the final executable.
 *   A routine can be declared `preserved`, which prevents a
     compiler from omitting it from the final executable, even
     if it determines it is not called by any other routine.
diff --git a/TODO.md b/TODO.md
index 1761bde..036555c 100644
--- a/TODO.md
+++ b/TODO.md
@@ -102,9 +102,6 @@ Once we have a call graph we can omit routines that we're sure aren't called.
 This would let us use include-files and standard-libraries nicely: any
 routines they define, but that you don't use, don't get included.
 
-Analyzing the set of possible routines that a vector can take on would help
-this immensely.
-
 Implementation
 --------------
 
diff --git a/src/sixtypical/callgraph.py b/src/sixtypical/callgraph.py
index bf8b39d..b91e312 100644
--- a/src/sixtypical/callgraph.py
+++ b/src/sixtypical/callgraph.py
@@ -8,6 +8,15 @@ def find_routines_matching_type(program, type_):
     return [r for r in program.routines if RoutineType.executable_types_compatible(r.routine_type, type_)]
 
 
+def mark_as_reachable(graph, routine_name):
+    node = graph[routine_name]
+    if node.get('reachable', False):
+        return
+    node['reachable'] = True
+    for next_routine_name in node['potentially-calls']:
+        mark_as_reachable(graph, next_routine_name)
+
+
 def construct_callgraph(program):
     graph = {}
 
@@ -33,8 +42,19 @@ def construct_callgraph(program):
             potential_calls = node['potentially-calls']
             if routine.name in potential_calls:
                 potentially_called_by.append(name)
-        if getattr(routine, 'preserved', None) or routine.name == 'main':
-            potentially_called_by.append('*preserved*')
         graph[routine.name]['potentially-called-by'] = potentially_called_by
 
+    # Root set
+
+    root_set = set()
+
+    for routine in program.routines:
+        if getattr(routine, 'preserved', False) or routine.name == 'main':
+            root_set.add(routine)
+
+    # Reachability
+
+    for routine in root_set:
+        mark_as_reachable(graph, routine.name)
+
     return graph
diff --git a/tests/SixtyPical Callgraph.md b/tests/SixtyPical Callgraph.md
index 62d5ff6..b703511 100644
--- a/tests/SixtyPical Callgraph.md	
+++ b/tests/SixtyPical Callgraph.md	
@@ -11,22 +11,23 @@ called.
     -> Tests for functionality "Dump callgraph info for SixtyPical program"
 
 The `main` routine is always called.  The thing that it will
-be called by is the system, but the callgraph analyzer will
-simply consider it to be "marked as preserved".
+be called by is the system, but the callgraph analyzer simply
+considers it to be "reachable".
 
     | define main routine
     | {
     | }
     = {
     =     "main": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
-    =         "potentially-calls": []
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     }
     = }
 
 If a routine is called by another routine, this fact will be noted.
+If it is reachable (directly or indirectly) from `main`, this will
+be noted as well.
 
     | define main routine
     | {
@@ -38,25 +39,25 @@ If a routine is called by another routine, this fact will be noted.
     | }
     = {
     =     "main": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
+    =         "potentially-called-by": [],
     =         "potentially-calls": [
     =             "other"
-    =         ]
+    =         ],
+    =         "reachable": true
     =     },
     =     "other": {
     =         "potentially-called-by": [
     =             "main"
     =         ],
-    =         "potentially-calls": []
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     }
     = }
 
-If a routine is not called by another routine, and it is not `main`
-and it is not explicitly marked as preserved, this absence will be
-noted, and a compiler or linker will be permitted to omit it from
-the final executable.
+If a routine is not potentially called by any other routine that is
+ultimately potentially called by `main`, this absence will be noted
+— the routine will not be considered reachable — and a compiler or
+linker will be permitted to omit it from the final executable.
 
     | define main routine
     | {
@@ -67,10 +68,9 @@ the final executable.
     | }
     = {
     =     "main": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
-    =         "potentially-calls": []
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     },
     =     "other": {
     =         "potentially-called-by": [],
@@ -79,11 +79,11 @@ the final executable.
     = }
 
 If a routine is not called by another routine, but it is declared
-explicitly as `preserved`, then it will not be considered unused,
-and a compiler or linker will not be permitted to omit it from
-the final executable.  This is useful for interrupt routines and
-such that really are used by some part of the system, even if not
-directly by another SixtyPical routine.
+explicitly as `preserved`, then it will still be considered
+reachable, and a compiler or linker will not be permitted to omit it
+from the final executable.  This is useful for interrupt routines
+and such that really are used by some part of the system, even if
+not directly by another SixtyPical routine.
 
     | define main routine
     | {
@@ -94,22 +94,58 @@ directly by another SixtyPical routine.
     | }
     = {
     =     "main": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
-    =         "potentially-calls": []
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     },
     =     "other": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
-    =         "potentially-calls": []
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     }
     = }
 
-If two routines potentially call each other, this will be noted,
-even if nothing else potentially calls either of those routines.
-This may change in the future.
+If a routine is called from a preserved routine, that routine is
+reachable.
+
+    | define main routine
+    | {
+    | }
+    | 
+    | define other1 preserved routine
+    | {
+    |   call other2
+    | }
+    | 
+    | define other2 preserved routine
+    | {
+    | }
+    = {
+    =     "main": {
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
+    =     },
+    =     "other1": {
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [
+    =             "other2"
+    =         ],
+    =         "reachable": true
+    =     },
+    =     "other2": {
+    =         "potentially-called-by": [
+    =             "other1"
+    =         ],
+    =         "potentially-calls": [],
+    =         "reachable": true
+    =     }
+    = }
+
+If a group of routines potentially call each other, but neither is
+found to be reachable (directly or indirectly) from `main` or a
+`preserved` routine, the routines in the group will not be considered
+reachable.
 
     | define main routine
     | {
@@ -126,10 +162,9 @@ This may change in the future.
     | }
     = {
     =     "main": {
-    =         "potentially-called-by": [
-    =             "*preserved*"
-    =         ],
-    =         "potentially-calls": []
+    =         "potentially-called-by": [],
+    =         "potentially-calls": [],
+    =         "reachable": true
     =     },
     =     "other1": {
     =         "potentially-called-by": [