diff --git a/libstdc++-v3/ChangeLog b/libstdc++-v3/ChangeLog
index 438206b33a8..7c583dd726e 100644
--- a/libstdc++-v3/ChangeLog
+++ b/libstdc++-v3/ChangeLog
@@ -1,3 +1,11 @@
+2018-10-23  Jonathan Wakely  <jwakely@redhat.com>
+
+	PR libstdc++/87704
+	* include/bits/unique_ptr.h (unique_ptr::unique_ptr(nullptr_t)): Do
+	not delegate to default constructor.
+	(unique_ptr<T[], D>::unique_ptr(nullptr_t)): Likewise.
+	* testsuite/20_util/unique_ptr/cons/incomplete.cc: New test.
+
 2018-10-20  François Dumont  <fdumont@gcc.gnu.org>
 
 	* testsuite/util/testsuite_containers.h
diff --git a/libstdc++-v3/include/bits/unique_ptr.h b/libstdc++-v3/include/bits/unique_ptr.h
index 0717c1e2728..dcb866d37bc 100644
--- a/libstdc++-v3/include/bits/unique_ptr.h
+++ b/libstdc++-v3/include/bits/unique_ptr.h
@@ -195,7 +195,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       template<typename _Del = _Dp, typename = _DeleterConstraint<_Del>>
 	constexpr unique_ptr() noexcept
 	: _M_t()
-        { }
+	{ }
 
       /** Takes ownership of a pointer.
        *
@@ -244,7 +244,9 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 
       /// Creates a unique_ptr that owns nothing.
       template<typename _Del = _Dp, typename = _DeleterConstraint<_Del>>
-	constexpr unique_ptr(nullptr_t) noexcept : unique_ptr() { }
+	constexpr unique_ptr(nullptr_t) noexcept
+	: _M_t()
+	{ }
 
       // Move constructors.
 
@@ -472,7 +474,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       template<typename _Del = _Dp, typename = _DeleterConstraint<_Del>>
 	constexpr unique_ptr() noexcept
 	: _M_t()
-        { }
+	{ }
 
       /** Takes ownership of a pointer.
        *
@@ -535,7 +537,9 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 
       /// Creates a unique_ptr that owns nothing.
       template<typename _Del = _Dp, typename = _DeleterConstraint<_Del>>
-	constexpr unique_ptr(nullptr_t) noexcept : unique_ptr() { }
+	constexpr unique_ptr(nullptr_t) noexcept
+	: _M_t()
+        { }
 
       template<typename _Up, typename _Ep,
 	       typename = _Require<__safe_conversion_up<_Up, _Ep>>>
diff --git a/libstdc++-v3/testsuite/20_util/unique_ptr/cons/incomplete.cc b/libstdc++-v3/testsuite/20_util/unique_ptr/cons/incomplete.cc
new file mode 100644
index 00000000000..1a8f28838a1
--- /dev/null
+++ b/libstdc++-v3/testsuite/20_util/unique_ptr/cons/incomplete.cc
@@ -0,0 +1,32 @@
+// Copyright (C) 2018 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do compile { target c++11 } }
+
+#include <memory>
+
+struct Incomplete;
+
+void f(void** p)
+{
+  ::new (p[0]) std::unique_ptr<Incomplete>();
+  ::new (p[1]) std::unique_ptr<Incomplete[]>();
+
+  // PR libstdc++/87704
+  ::new (p[2]) std::unique_ptr<Incomplete>(nullptr);
+  ::new (p[3]) std::unique_ptr<Incomplete[]>(nullptr);
+}