diff --git a/rust/ql/lib/codeql/rust/controlflow/internal/Completion.qll b/rust/ql/lib/codeql/rust/controlflow/internal/Completion.qll
index b00a4047c1fb3..ecf688f03931e 100644
--- a/rust/ql/lib/codeql/rust/controlflow/internal/Completion.qll
+++ b/rust/ql/lib/codeql/rust/controlflow/internal/Completion.qll
@@ -1,11 +1,12 @@
-private import rust
+private import codeql.util.Boolean
 private import codeql.rust.controlflow.ControlFlowGraph
+private import rust
 private import SuccessorType
 private import SuccessorTypes
 
 private newtype TCompletion =
   TSimpleCompletion() or
-  TBooleanCompletion(boolean b) { b in [false, true] } or
+  TBooleanCompletion(Boolean b) or
   TReturnCompletion()
 
 /** A completion of a statement or an expression. */
@@ -82,3 +83,12 @@ class ReturnCompletion extends TReturnCompletion, Completion {
 
   override string toString() { result = "return" }
 }
+
+/** Hold if `c` represents normal evaluation of a statement or an expression. */
+predicate completionIsNormal(Completion c) { c instanceof NormalCompletion }
+
+/** Hold if `c` represents simple and normal evaluation of a statement or an expression. */
+predicate completionIsSimple(Completion c) { c instanceof SimpleCompletion }
+
+/** Holds if `c` is a valid completion for `n`. */
+predicate completionIsValidFor(Completion c, AstNode n) { c.isValidFor(n) }
diff --git a/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImpl.qll b/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImpl.qll
index 386dd92d498bc..5586368a7d619 100644
--- a/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImpl.qll
+++ b/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImpl.qll
@@ -1 +1,47 @@
+private import rust
 import ControlFlowGraphImplSpecific::CfgImpl
+import Completion
+
+class CallTree extends StandardPostOrderTree instanceof Call {
+  override ControlFlowTree getChildNode(int i) { result = super.getArg(i) }
+}
+
+class BinaryOpTree extends StandardPostOrderTree instanceof BinaryOp {
+  override ControlFlowTree getChildNode(int i) {
+    i = 0 and result = super.getLhs()
+    or
+    i = 1 and result = super.getRhs()
+  }
+}
+
+class IfTree extends PostOrderTree instanceof If {
+  override predicate first(AstNode node) { first(super.getCondition(), node) }
+
+  override predicate propagatesAbnormal(AstNode child) { none() }
+
+  override predicate succ(AstNode pred, AstNode succ, Completion c) {
+    // Edges from the condition to each branch
+    last(super.getCondition(), pred, c) and
+    (
+      first(super.getThen(), succ) and c.(BooleanCompletion).getValue() = true
+      or
+      first(super.getElse(), succ) and c.(BooleanCompletion).getValue() = false
+    )
+    or
+    // An edge from the then branch to the last node
+    last(super.getThen(), pred, c) and
+    succ = this and
+    completionIsSimple(c)
+    or
+    // An edge from the else branch to the last node
+    last(super.getElse(), pred, c) and
+    succ = this and
+    completionIsSimple(c)
+  }
+}
+
+class LetTree extends StandardPostOrderTree instanceof Let {
+  override ControlFlowTree getChildNode(int i) { i = 0 and result = super.getExpr() }
+}
+
+class LiteralTree extends LeafTree instanceof Literal { }
diff --git a/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImplSpecific.qll b/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImplSpecific.qll
index 854bbcc7d73f8..9a6f615dab429 100644
--- a/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImplSpecific.qll
+++ b/rust/ql/lib/codeql/rust/controlflow/internal/ControlFlowGraphImplSpecific.qll
@@ -11,11 +11,11 @@ module CfgInput implements InputSig<Rust::Location> {
 
   class Completion = C::Completion;
 
-  predicate completionIsNormal(Completion c) { c instanceof C::NormalCompletion }
+  predicate completionIsNormal = C::completionIsNormal/1;
 
-  predicate completionIsSimple(Completion c) { c instanceof C::SimpleCompletion }
+  predicate completionIsSimple = C::completionIsSimple/1;
 
-  predicate completionIsValidFor(Completion c, AstNode e) { c.isValidFor(e) }
+  predicate completionIsValidFor = C::completionIsValidFor/2;
 
   /** An AST node with an associated control-flow graph. */
   class CfgScope = Scope::CfgScope;
diff --git a/rust/ql/lib/codeql/rust/controlflow/internal/SuccessorType.qll b/rust/ql/lib/codeql/rust/controlflow/internal/SuccessorType.qll
index 255ac8c796555..6a58482348a69 100644
--- a/rust/ql/lib/codeql/rust/controlflow/internal/SuccessorType.qll
+++ b/rust/ql/lib/codeql/rust/controlflow/internal/SuccessorType.qll
@@ -1,7 +1,9 @@
+private import codeql.util.Boolean
+
 cached
 newtype TSuccessorType =
   TSuccessorSuccessor() or
-  TBooleanSuccessor(boolean b) { b in [false, true] } or
+  TBooleanSuccessor(Boolean b) or
   TReturnSuccessor()
 
 /** The type of a control flow successor. */