diff --git a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisConstantSpecific.qll b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisConstantSpecific.qll
index 31832a7bd69..e9a7dc836e4 100644
--- a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisConstantSpecific.qll
+++ b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisConstantSpecific.qll
@@ -25,4 +25,8 @@ module CppLangImplConstant implements LangSig<Sem, FloatDelta> {
    * Holds if `e2 >= e1 + delta` (if `upper = false`) or `e2 <= e1 + delta` (if `upper = true`).
    */
   predicate additionalBoundFlowStep(SemExpr e2, SemExpr e1, float delta, boolean upper) { none() }
+
+  predicate includeConstantBounds() { any() }
+
+  predicate includeRelativeBounds() { none() }
 }
diff --git a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisImpl.qll b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisImpl.qll
index 3b153f001d6..a19baf2eea7 100644
--- a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisImpl.qll
+++ b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisImpl.qll
@@ -173,11 +173,11 @@ private module ModulusAnalysisInstantiated implements ModulusAnalysisSig<Sem> {
 }
 
 module ConstantStage =
-  RangeStage<SemLocation, Sem, FloatDelta, ConstantBounds, FloatOverflow, CppLangImplConstant,
+  RangeStage<SemLocation, Sem, FloatDelta, AllBounds, FloatOverflow, CppLangImplConstant,
     SignAnalysis, ModulusAnalysisInstantiated>;
 
 module RelativeStage =
-  RangeStage<SemLocation, Sem, FloatDelta, RelativeBounds, FloatOverflow, CppLangImplRelative,
+  RangeStage<SemLocation, Sem, FloatDelta, AllBounds, FloatOverflow, CppLangImplRelative,
     SignAnalysis, ModulusAnalysisInstantiated>;
 
 private newtype TSemReason =
diff --git a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisRelativeSpecific.qll b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisRelativeSpecific.qll
index 4f88f5ca355..3774d47db8b 100644
--- a/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisRelativeSpecific.qll
+++ b/cpp/ql/lib/semmle/code/cpp/rangeanalysis/new/internal/semantic/analysis/RangeAnalysisRelativeSpecific.qll
@@ -57,4 +57,8 @@ module CppLangImplRelative implements LangSig<Sem, FloatDelta> {
    * Holds if `e2 >= e1 + delta` (if `upper = false`) or `e2 <= e1 + delta` (if `upper = true`).
    */
   predicate additionalBoundFlowStep(SemExpr e2, SemExpr e1, float delta, boolean upper) { none() }
+
+  predicate includeConstantBounds() { none() }
+
+  predicate includeRelativeBounds() { any() }
 }
diff --git a/shared/rangeanalysis/codeql/rangeanalysis/RangeAnalysis.qll b/shared/rangeanalysis/codeql/rangeanalysis/RangeAnalysis.qll
index a8801c58404..55c0e3b432e 100644
--- a/shared/rangeanalysis/codeql/rangeanalysis/RangeAnalysis.qll
+++ b/shared/rangeanalysis/codeql/rangeanalysis/RangeAnalysis.qll
@@ -289,6 +289,10 @@ signature module LangSig<Semantic Sem, DeltaSig D> {
   predicate ignoreExprBound(Sem::Expr e);
 
   default predicate javaCompatibility() { none() }
+
+  default predicate includeConstantBounds() { any() }
+
+  default predicate includeRelativeBounds() { any() }
 }
 
 signature module BoundSig<LocationSig Location, Semantic Sem, DeltaSig D> {
@@ -983,6 +987,13 @@ module RangeStage<
     )
   }
 
+  private predicate includeBound(SemBound b) {
+    // always include phi bounds
+    b.(SemSsaBound).getVariable() instanceof Sem::SsaPhiNode
+    or
+    if b instanceof SemZeroBound then includeConstantBounds() else includeRelativeBounds()
+  }
+
   /**
    * Holds if `e` has an upper (for `upper = true`) or lower
    * (for `upper = false`) bound of `b`.
@@ -1122,13 +1133,15 @@ module RangeStage<
       (upper = true or upper = false) and
       fromBackEdge = false and
       origdelta = delta and
-      reason = TSemNoReason()
+      reason = TSemNoReason() and
+      includeBound(b)
       or
       baseBound(e, delta, upper) and
       b instanceof SemZeroBound and
       fromBackEdge = false and
       origdelta = delta and
-      reason = TSemNoReason()
+      reason = TSemNoReason() and
+      includeBound(b)
       or
       exists(Sem::SsaVariable v, SsaReadPositionBlock bb |
         boundedSsa(v, b, delta, bb, upper, fromBackEdge, origdelta, reason) and