diff --git a/modules/beast_asio/async/ComposedAsyncOperation.h b/modules/beast_asio/async/ComposedAsyncOperation.h
index 54fffe055..a5884ccb1 100644
--- a/modules/beast_asio/async/ComposedAsyncOperation.h
+++ b/modules/beast_asio/async/ComposedAsyncOperation.h
@@ -87,7 +87,7 @@ protected:
 #endif
     }
 
-    void destroy ()
+    void destroy () const
     {
         delete this;
     }
diff --git a/modules/beast_asio/async/SharedHandlerType.h b/modules/beast_asio/async/SharedHandlerType.h
index 40de9f326..89d9f3c4d 100644
--- a/modules/beast_asio/async/SharedHandlerType.h
+++ b/modules/beast_asio/async/SharedHandlerType.h
@@ -85,11 +85,13 @@ protected:
     // the size from the original allocation, which we saved at
     // the time of construction.
     //
-    void destroy ()
+    void destroy () const
     {
         Handler local (BOOST_ASIO_MOVE_CAST(Handler)(m_handler));
         std::size_t const size (m_size);
-        SharedHandler* const shared (static_cast <SharedHandler*>(this));
+        SharedHandler* const shared (
+            const_cast <SharedHandler*> (
+                static_cast <SharedHandler const*>(this)));
         shared->~SharedHandler ();
         boost_asio_handler_alloc_helpers::
             deallocate <Handler> (shared, size, local);
@@ -109,7 +111,7 @@ protected:
 
 protected:
     std::size_t const m_size;
-    Handler m_handler;
+    Handler mutable m_handler;
 };
 
 //--------------------------------------------------------------------------
diff --git a/modules/beast_core/memory/SharedObject.h b/modules/beast_core/memory/SharedObject.h
index c2853db0a..8efd00aeb 100644
--- a/modules/beast_core/memory/SharedObject.h
+++ b/modules/beast_core/memory/SharedObject.h
@@ -65,7 +65,7 @@ public:
         This is done automatically by the smart pointer, but is public just
         in case it's needed for nefarious purposes.
     */
-    inline void incReferenceCount() noexcept
+    inline void incReferenceCount() const noexcept
     {
         ++refCount;
     }
@@ -79,7 +79,7 @@ public:
         The return value indicates if the reference count dropped to zero,
         so callers who know the derived type can use the ContainerDeletePolicy.
     */
-    void decReferenceCount ()
+    void decReferenceCount () const
     {
         bassert (getReferenceCount() > 0);
         if (--refCount == 0)
@@ -109,7 +109,7 @@ protected:
     /** Destroy the object.
         Derived classes can override this for different behaviors.
     */
-    virtual void destroy ()
+    virtual void destroy () const
     {
         delete this;
     }
@@ -124,7 +124,7 @@ protected:
 
 private:
     //==============================================================================
-    Atomic <int> refCount;
+    Atomic <int> mutable refCount;
 };
 
 //==============================================================================
@@ -184,7 +184,7 @@ protected:
         bassert (getReferenceCount() == 0);
     }
 
-    virtual void destroy ()
+    virtual void destroy () const
     {
         delete this;
     }