diff --git a/compiler/src/dmd/clone.d b/compiler/src/dmd/clone.d
index ca7f398ae7..e4060d4e39 100644
--- a/compiler/src/dmd/clone.d
+++ b/compiler/src/dmd/clone.d
@@ -1571,7 +1571,7 @@ private Statement generateCopyCtorBody(StructDeclaration sd)
  *  `true` if one needs to be generated
  *  `false` otherwise
  */
-private bool needCopyCtor(StructDeclaration sd, out bool hasCpCtor)
+bool needCopyCtor(StructDeclaration sd, out bool hasCpCtor)
 {
     if (global.errors)
         return false;
diff --git a/compiler/src/dmd/dstruct.d b/compiler/src/dmd/dstruct.d
index 0e0a1f52f8..49411c6975 100644
--- a/compiler/src/dmd/dstruct.d
+++ b/compiler/src/dmd/dstruct.d
@@ -434,7 +434,11 @@ extern (C++) class StructDeclaration : AggregateDeclaration
 
         ispod = ThreeState.yes;
 
-        if (enclosing || postblit || dtor || hasCopyCtor)
+        import dmd.clone;
+        bool hasCpCtorLocal;
+        needCopyCtor(this, hasCpCtorLocal);
+
+        if (enclosing || search(this, loc, Id.postblit) || search(this, loc, Id.dtor) || hasCpCtorLocal)
         {
             ispod = ThreeState.no;
             return false;
diff --git a/compiler/test/compilable/issue20339.d b/compiler/test/compilable/issue20339.d
new file mode 100644
index 0000000000..3d5bdd80a0
--- /dev/null
+++ b/compiler/test/compilable/issue20339.d
@@ -0,0 +1,44 @@
+/*
+TEST_OUTPUT:
+---
+4
+false
+false
+---
+*/
+
+// https://issues.dlang.org/show_bug.cgi?id=20339
+
+struct S
+{
+    pragma(msg, cast(int)S.sizeof);
+
+    this(this){}
+    ~this(){}
+
+    int f;
+}
+
+static assert(__traits(isPOD, S) == false);
+
+
+pragma(msg, __traits(isPOD, T));
+
+struct T
+{
+    this(this){}
+    ~this(){}
+}
+
+static assert(__traits(isPOD, T) == false);
+
+
+struct U
+{
+    pragma(msg, __traits(isPOD, U));
+
+    this(this){}
+    ~this(){}
+}
+
+static assert(__traits(isPOD, U) == false);
diff --git a/compiler/test/runnable_cxx/extra-files/test24292.cpp b/compiler/test/runnable_cxx/extra-files/test24292.cpp
new file mode 100644
index 0000000000..2fab9afbbd
--- /dev/null
+++ b/compiler/test/runnable_cxx/extra-files/test24292.cpp
@@ -0,0 +1,46 @@
+template<class T>
+struct List
+{
+    T* begin;
+};
+
+struct StructWithDestructor
+{
+    ~StructWithDestructor();
+
+    int i;
+};
+
+struct StructWithCopyCtor
+{
+    StructWithCopyCtor();
+    StructWithCopyCtor(const StructWithCopyCtor &other);
+
+    int i;
+};
+
+StructWithDestructor::~StructWithDestructor()
+{
+}
+
+StructWithCopyCtor::StructWithCopyCtor()
+{
+}
+
+StructWithCopyCtor::StructWithCopyCtor(const StructWithCopyCtor &other) : i(other.i)
+{
+}
+
+StructWithDestructor getStructWithDestructor()
+{
+    StructWithDestructor r;
+    r.i = 12345;
+    return r;
+}
+
+StructWithCopyCtor getStructWithCopyCtor()
+{
+    StructWithCopyCtor r;
+    r.i = 54321;
+    return r;
+}
diff --git a/compiler/test/runnable_cxx/test24292.d b/compiler/test/runnable_cxx/test24292.d
new file mode 100644
index 0000000000..b71f925639
--- /dev/null
+++ b/compiler/test/runnable_cxx/test24292.d
@@ -0,0 +1,50 @@
+// EXTRA_CPP_SOURCES: test24292.cpp
+
+extern(C++) struct List(T)
+{
+    // Any of the following static ifs can trigger the problem.
+    static if (T.sizeof > 4) {}
+    static if (__traits(isZeroInit, T)) {}
+    static if (__traits(isPOD, T)) {}
+
+    T* begin;
+}
+
+extern(C++) struct StructWithDestructor
+{
+    ~this();
+
+    alias L = List!StructWithDestructor;
+    int i;
+}
+
+extern(C++) struct StructWithCopyCtor
+{
+    this(ref const(StructWithCopyCtor));
+
+    alias L = List!StructWithCopyCtor;
+    int i;
+}
+
+extern(D) struct StructWithPostblit
+{
+    this(this) {}
+
+    alias L = List!StructWithPostblit;
+    int i;
+}
+
+static assert(!__traits(isPOD, StructWithDestructor));
+static assert(!__traits(isPOD, StructWithCopyCtor));
+static assert(!__traits(isPOD, StructWithPostblit));
+
+extern(C++) StructWithDestructor getStructWithDestructor();
+extern(C++) StructWithCopyCtor getStructWithCopyCtor();
+
+void main()
+{
+    StructWithDestructor structWithDestructor = getStructWithDestructor();
+    assert(structWithDestructor.i == 12345);
+    StructWithCopyCtor structWithCopyCtor = getStructWithCopyCtor();
+    assert(structWithCopyCtor.i == 54321);
+}