diff --git a/javascript/ql/src/semmle/javascript/PackageExports.qll b/javascript/ql/src/semmle/javascript/PackageExports.qll
index c66585344599..c225e5a733be 100644
--- a/javascript/ql/src/semmle/javascript/PackageExports.qll
+++ b/javascript/ql/src/semmle/javascript/PackageExports.qll
@@ -5,11 +5,14 @@
  */
 
 import javascript
+private import semmle.javascript.internal.CachedStages
 
 /**
  * Gets a parameter that is a library input to a top-level package.
  */
+cached
 DataFlow::ParameterNode getALibraryInputParameter() {
+  Stages::Taint::ref() and
   exists(int bound, DataFlow::FunctionNode func |
     func = getAValueExportedByPackage().getABoundFunctionValue(bound) and
     result = func.getParameter(any(int arg | arg >= bound))
diff --git a/javascript/ql/src/semmle/javascript/dataflow/DataFlow.qll b/javascript/ql/src/semmle/javascript/dataflow/DataFlow.qll
index 2bcee954cbc0..c73c894ca4b5 100644
--- a/javascript/ql/src/semmle/javascript/dataflow/DataFlow.qll
+++ b/javascript/ql/src/semmle/javascript/dataflow/DataFlow.qll
@@ -255,7 +255,9 @@ module DataFlow {
      * Holds if this node is annotated with the given named type,
      * or is declared as a subtype thereof, or is a union or intersection containing such a type.
      */
+    cached
     predicate hasUnderlyingType(string globalName) {
+      Stages::TypeTracking::ref() and
       getType().hasUnderlyingType(globalName)
       or
       getFallbackTypeAnnotation().getAnUnderlyingType().hasQualifiedName(globalName)
@@ -265,7 +267,9 @@ module DataFlow {
      * Holds if this node is annotated with the given named type,
      * or is declared as a subtype thereof, or is a union or intersection containing such a type.
      */
+    cached
     predicate hasUnderlyingType(string moduleName, string typeName) {
+      Stages::TypeTracking::ref() and
       getType().hasUnderlyingType(moduleName, typeName)
       or
       getFallbackTypeAnnotation().getAnUnderlyingType().hasQualifiedName(moduleName, typeName)
diff --git a/javascript/ql/src/semmle/javascript/dataflow/internal/StepSummary.qll b/javascript/ql/src/semmle/javascript/dataflow/internal/StepSummary.qll
index 5869444053fb..2c1362c871d1 100644
--- a/javascript/ql/src/semmle/javascript/dataflow/internal/StepSummary.qll
+++ b/javascript/ql/src/semmle/javascript/dataflow/internal/StepSummary.qll
@@ -53,49 +53,11 @@ private module Cached {
   predicate step(DataFlow::SourceNode pred, DataFlow::SourceNode succ, StepSummary summary) {
     exists(DataFlow::Node mid | pred.flowsTo(mid) | StepSummary::smallstep(mid, succ, summary))
   }
-}
-
-import Cached::Public
-
-class OptionalPropertyName extends string {
-  OptionalPropertyName() { this instanceof PropertyName or this = "" }
-}
-
-/**
- * INTERNAL: Use `TypeTracker` or `TypeBackTracker` instead.
- *
- * A description of a step on an inter-procedural data flow path.
- */
-class StepSummary extends TStepSummary {
-  /** Gets a textual representation of this step summary. */
-  string toString() {
-    this instanceof LevelStep and result = "level"
-    or
-    this instanceof CallStep and result = "call"
-    or
-    this instanceof ReturnStep and result = "return"
-    or
-    exists(string prop | this = StoreStep(prop) | result = "store " + prop)
-    or
-    exists(string prop | this = LoadStep(prop) | result = "load " + prop)
-    or
-    exists(string prop | this = CopyStep(prop) | result = "copy " + prop)
-    or
-    exists(string fromProp, string toProp | this = LoadStoreStep(fromProp, toProp) |
-      result = "load " + fromProp + " and store to " + toProp
-    )
-  }
-}
-
-module StepSummary {
-  /**
-   * INTERNAL: Use `SourceNode.track()` or `SourceNode.backtrack()` instead.
-   */
-  predicate step = Cached::step/3;
 
   /**
    * INTERNAL: Use `TypeBackTracker.smallstep()` instead.
    */
+  cached
   predicate smallstep(DataFlow::Node pred, DataFlow::Node succ, StepSummary summary) {
     // Flow through properties of objects
     propertyFlowStep(pred, succ) and
@@ -194,3 +156,47 @@ module StepSummary {
     )
   }
 }
+
+import Cached::Public
+
+class OptionalPropertyName extends string {
+  OptionalPropertyName() { this instanceof PropertyName or this = "" }
+}
+
+/**
+ * INTERNAL: Use `TypeTracker` or `TypeBackTracker` instead.
+ *
+ * A description of a step on an inter-procedural data flow path.
+ */
+class StepSummary extends TStepSummary {
+  /** Gets a textual representation of this step summary. */
+  string toString() {
+    this instanceof LevelStep and result = "level"
+    or
+    this instanceof CallStep and result = "call"
+    or
+    this instanceof ReturnStep and result = "return"
+    or
+    exists(string prop | this = StoreStep(prop) | result = "store " + prop)
+    or
+    exists(string prop | this = LoadStep(prop) | result = "load " + prop)
+    or
+    exists(string prop | this = CopyStep(prop) | result = "copy " + prop)
+    or
+    exists(string fromProp, string toProp | this = LoadStoreStep(fromProp, toProp) |
+      result = "load " + fromProp + " and store to " + toProp
+    )
+  }
+}
+
+module StepSummary {
+  /**
+   * INTERNAL: Use `SourceNode.track()` or `SourceNode.backtrack()` instead.
+   */
+  predicate step = Cached::step/3;
+
+  /**
+   * INTERNAL: Use `TypeBackTracker.smallstep()` instead.
+   */
+  predicate smallstep = Cached::smallstep/3;
+}
diff --git a/javascript/ql/src/semmle/javascript/internal/CachedStages.qll b/javascript/ql/src/semmle/javascript/internal/CachedStages.qll
index a48cb8ed5e03..40b5e5ba6267 100644
--- a/javascript/ql/src/semmle/javascript/internal/CachedStages.qll
+++ b/javascript/ql/src/semmle/javascript/internal/CachedStages.qll
@@ -198,6 +198,10 @@ module Stages {
       exists(any(DataFlow::TypeBackTracker t).prepend(_))
       or
       DataFlow::functionForwardingStep(_, _)
+      or
+      any(DataFlow::Node node).hasUnderlyingType(_)
+      or
+      any(DataFlow::Node node).hasUnderlyingType(_, _)
     }
   }
 
@@ -232,6 +236,8 @@ module Stages {
    */
   cached
   module Taint {
+    private import semmle.javascript.PackageExports as Exports
+
     /**
      * Always holds.
      * Ensures that a predicate is evaluated as part of the Taint stage.
@@ -250,6 +256,8 @@ module Stages {
       TaintTracking::heapStep(_, _)
       or
       exists(RemoteFlowSource r)
+      or
+      exists(Exports::getALibraryInputParameter())
     }
   }
 }