diff --git a/src/intptrcast.rs b/src/intptrcast.rs
index 8395cdc273..4850945b4e 100644
--- a/src/intptrcast.rs
+++ b/src/intptrcast.rs
@@ -105,6 +105,8 @@ impl<'mir, 'tcx> GlobalStateInner {
         trace!("Exposing allocation id {:?}", alloc_id);
 
         let mut global_state = ecx.machine.intptrcast.borrow_mut();
+        // In legacy and strict mode, we don't need this, so we can save some cycles
+        // by not tracking it.
         if global_state.provenance_mode == ProvenanceMode::Permissive {
             global_state.exposed.insert(alloc_id);
         }
@@ -118,12 +120,17 @@ impl<'mir, 'tcx> GlobalStateInner {
 
         let global_state = ecx.machine.intptrcast.borrow();
 
-        // In legacy mode, we have to support int2ptr transmutes,
-        // so just pretend they do the same thing as a cast.
-        if global_state.provenance_mode == ProvenanceMode::Legacy {
-            Self::ptr_from_addr_cast(ecx, addr)
-        } else {
-            Pointer::new(None, Size::from_bytes(addr))
+        match global_state.provenance_mode {
+            ProvenanceMode::Legacy => {
+                // In legacy mode, we have to support int2ptr transmutes,
+                // so just pretend they do the same thing as a cast.
+                Self::ptr_from_addr_cast(ecx, addr)
+            }
+            ProvenanceMode::Permissive | ProvenanceMode::Strict => {
+                // Both of these modes consider transmuted pointers to be "invalid" (`None`
+                // provenance).
+                Pointer::new(None, Size::from_bytes(addr))
+            }
         }
     }
 
@@ -135,18 +142,26 @@ impl<'mir, 'tcx> GlobalStateInner {
 
         let global_state = ecx.machine.intptrcast.borrow();
 
-        if global_state.provenance_mode == ProvenanceMode::Strict {
-            Pointer::new(None, Size::from_bytes(addr))
-        } else if global_state.provenance_mode == ProvenanceMode::Legacy {
-            let alloc_id = Self::alloc_id_from_addr(ecx, addr);
-
-            Pointer::new(
-                alloc_id
-                    .map(|alloc_id| Tag::Concrete(ConcreteTag { alloc_id, sb: SbTag::Untagged })),
-                Size::from_bytes(addr),
-            )
-        } else {
-            Pointer::new(Some(Tag::Wildcard), Size::from_bytes(addr))
+        match global_state.provenance_mode {
+            ProvenanceMode::Legacy => {
+                // Determine the allocation this points to at cast time.
+                let alloc_id = Self::alloc_id_from_addr(ecx, addr);
+                Pointer::new(
+                    alloc_id.map(|alloc_id| {
+                        Tag::Concrete(ConcreteTag { alloc_id, sb: SbTag::Untagged })
+                    }),
+                    Size::from_bytes(addr),
+                )
+            }
+            ProvenanceMode::Strict => {
+                // We don't support int2ptr casts in this mode (i.e., we treat them like
+                // transmutes).
+                Pointer::new(None, Size::from_bytes(addr))
+            }
+            ProvenanceMode::Permissive => {
+                // This is how wildcard pointers are born.
+                Pointer::new(Some(Tag::Wildcard), Size::from_bytes(addr))
+            }
         }
     }
 
@@ -215,6 +230,8 @@ impl<'mir, 'tcx> GlobalStateInner {
         let alloc_id = if let Tag::Concrete(concrete) = tag {
             concrete.alloc_id
         } else {
+            // A wildcard pointer.
+            assert_eq!(ecx.machine.intptrcast.borrow().provenance_mode, ProvenanceMode::Permissive);
             GlobalStateInner::alloc_id_from_addr(ecx, addr.bytes())?
         };
 
diff --git a/src/machine.rs b/src/machine.rs
index 12a32d81b5..0972699e72 100644
--- a/src/machine.rs
+++ b/src/machine.rs
@@ -652,19 +652,18 @@ impl<'mir, 'tcx> Machine<'mir, 'tcx> for Evaluator<'mir, 'tcx> {
         intptrcast::GlobalStateInner::ptr_from_addr_transmute(ecx, addr)
     }
 
-    #[inline(always)]
     fn expose_ptr(
         ecx: &mut InterpCx<'mir, 'tcx, Self>,
         ptr: Pointer<Self::PointerTag>,
     ) -> InterpResult<'tcx> {
-        let tag = ptr.provenance;
-
-        if let Tag::Concrete(concrete) = tag {
-            intptrcast::GlobalStateInner::expose_addr(ecx, concrete.alloc_id);
+        match ptr.provenance {
+            Tag::Concrete(concrete) =>
+                intptrcast::GlobalStateInner::expose_addr(ecx, concrete.alloc_id),
+            Tag::Wildcard => {
+                // No need to do anything for wildcard pointers as
+                // their provenances have already been previously exposed.
+            }
         }
-
-        // No need to do anything for wildcard pointers as
-        // their provenances have already been previously exposed.
         Ok(())
     }
 
@@ -676,12 +675,13 @@ impl<'mir, 'tcx> Machine<'mir, 'tcx> for Evaluator<'mir, 'tcx> {
     ) -> Option<(AllocId, Size, Self::TagExtra)> {
         let rel = intptrcast::GlobalStateInner::abs_ptr_to_rel(ecx, ptr);
 
-        let sb = match ptr.provenance {
-            Tag::Concrete(ConcreteTag { sb, .. }) => sb,
-            Tag::Wildcard => SbTag::Untagged,
-        };
-
-        rel.map(|(alloc_id, size)| (alloc_id, size, sb))
+        rel.map(|(alloc_id, size)| {
+            let sb = match ptr.provenance {
+                Tag::Concrete(ConcreteTag { sb, .. }) => sb,
+                Tag::Wildcard => SbTag::Untagged,
+            };
+            (alloc_id, size, sb)
+        })
     }
 
     #[inline(always)]