diff --git a/compiler/rustc_const_eval/src/interpret/eval_context.rs b/compiler/rustc_const_eval/src/interpret/eval_context.rs
index 7c2100fcbe38a..c1daa2fac338e 100644
--- a/compiler/rustc_const_eval/src/interpret/eval_context.rs
+++ b/compiler/rustc_const_eval/src/interpret/eval_context.rs
@@ -1103,11 +1103,9 @@ impl<'tcx, M: Machine<'tcx>> InterpCx<'tcx, M> {
             Operand::Immediate(Immediate::Uninit)
         });
 
-        // StorageLive expects the local to be dead, and marks it live.
+        // If the local is already live, deallocate its old memory.
         let old = mem::replace(&mut self.frame_mut().locals[local].value, local_val);
-        if !matches!(old, LocalValue::Dead) {
-            throw_ub_custom!(fluent::const_eval_double_storage_live);
-        }
+        self.deallocate_local(old)?;
         Ok(())
     }
 
@@ -1121,7 +1119,7 @@ impl<'tcx, M: Machine<'tcx>> InterpCx<'tcx, M> {
         assert!(local != mir::RETURN_PLACE, "Cannot make return place dead");
         trace!("{:?} is now dead", local);
 
-        // It is entirely okay for this local to be already dead (at least that's how we currently generate MIR)
+        // If the local is already dead, this is a NOP.
         let old = mem::replace(&mut self.frame_mut().locals[local].value, LocalValue::Dead);
         self.deallocate_local(old)?;
         Ok(())
diff --git a/compiler/rustc_middle/src/mir/syntax.rs b/compiler/rustc_middle/src/mir/syntax.rs
index ebe77a1abfd8b..9855c72197edc 100644
--- a/compiler/rustc_middle/src/mir/syntax.rs
+++ b/compiler/rustc_middle/src/mir/syntax.rs
@@ -361,16 +361,19 @@ pub enum StatementKind<'tcx> {
     /// At any point during the execution of a function, each local is either allocated or
     /// unallocated. Except as noted below, all locals except function parameters are initially
     /// unallocated. `StorageLive` statements cause memory to be allocated for the local while
-    /// `StorageDead` statements cause the memory to be freed. Using a local in any way (not only
-    /// reading/writing from it) while it is unallocated is UB.
+    /// `StorageDead` statements cause the memory to be freed. In other words,
+    /// `StorageLive`/`StorageDead` act like the heap operations `allocate`/`deallocate`, but for
+    /// stack-allocated local variables. Using a local in any way (not only reading/writing from it)
+    /// while it is unallocated is UB.
     ///
     /// Some locals have no `StorageLive` or `StorageDead` statements within the entire MIR body.
     /// These locals are implicitly allocated for the full duration of the function. There is a
     /// convenience method at `rustc_mir_dataflow::storage::always_storage_live_locals` for
     /// computing these locals.
     ///
-    /// If the local is already allocated, calling `StorageLive` again is UB. However, for an
-    /// unallocated local an additional `StorageDead` all is simply a nop.
+    /// If the local is already allocated, calling `StorageLive` again will implicitly free the
+    /// local and then allocate fresh uninitilized memory. If a local is already deallocated,
+    /// calling `StorageDead` again is a NOP.
     StorageLive(Local),
 
     /// See `StorageLive` above.