diff --git a/gnu/packages/commencement.scm b/gnu/packages/commencement.scm
index 851bb02163..473d6b8345 100644
--- a/gnu/packages/commencement.scm
+++ b/gnu/packages/commencement.scm
@@ -1,5 +1,5 @@
 ;;; GNU Guix --- Functional package management for GNU
-;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Ludovic Courtès <ludo@gnu.org>
+;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Ludovic Courtès <ludo@gnu.org>
 ;;; Copyright © 2014 Andreas Enge <andreas@enge.fr>
 ;;; Copyright © 2012 Nikita Karetnikov <nikita@karetnikov.org>
 ;;; Copyright © 2014, 2015, 2017 Mark H Weaver <mhw@netris.org>
@@ -2303,15 +2303,6 @@ exec ~a/bin/~a-~a -B~a/lib -Wl,-dynamic-linker -Wl,~a/~a \"$@\"~%"
                                            char-set:letter)
                                          ,(package-name lib)))
                              (list gmp-6.0 mpfr mpc))
-                      #t)))
-                (add-before 'configure 'treat-glibc-as-system-header
-                  (lambda* (#:key inputs #:allow-other-keys)
-                    (let ((libc (assoc-ref inputs "libc")))
-                      ;; Make sure Glibc is treated as a "system header" so
-                      ;; #include_next does the right thing.
-                      (for-each (lambda (var)
-                                  (setenv var (string-append libc "/include")))
-                                '("C_INCLUDE_PATH" "CPLUS_INCLUDE_PATH"))
                       #t))))))))
 
     ;; This time we want Texinfo, so we get the manual.  Add
diff --git a/gnu/packages/gcc.scm b/gnu/packages/gcc.scm
index 40cc9ed631..4c4b63dbd1 100644
--- a/gnu/packages/gcc.scm
+++ b/gnu/packages/gcc.scm
@@ -1,5 +1,5 @@
 ;;; GNU Guix --- Functional package management for GNU
-;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Ludovic Courtès <ludo@gnu.org>
+;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Ludovic Courtès <ludo@gnu.org>
 ;;; Copyright © 2014, 2015, 2018 Mark H Weaver <mhw@netris.org>
 ;;; Copyright © 2014, 2015, 2016, 2017, 2019 Ricardo Wurmus <rekado@elephly.net>
 ;;; Copyright © 2015 Andreas Enge <andreas@enge.fr>
@@ -340,7 +340,9 @@ where the OS part is overloaded to denote a specific ABI---into GCC
                (files '("include")))
               (search-path-specification
                (variable "CPLUS_INCLUDE_PATH")
-               (files '("include")))
+               ;; Add 'include/c++' here so that <cstdlib>'s "#include_next
+               ;; <stdlib.h>" finds GCC's <stdlib.h>, not libc's.
+               (files '("include/c++" "include")))
               (search-path-specification
                (variable "LIBRARY_PATH")
                (files '("lib" "lib64")))))
@@ -476,17 +478,7 @@ Go.  It also includes runtime support libraries for these languages.")
                                        "gcc-5.0-libvtv-runpath.patch"))))
     (inputs
      `(("isl" ,isl)
-       ,@(package-inputs gcc-4.7)))
-
-    (native-search-paths
-     ;; We have to use 'CPATH' for GCC > 5, not 'C_INCLUDE_PATH' & co., due to
-     ;; <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70129>.
-     (list (search-path-specification
-            (variable "CPATH")
-            (files '("include")))
-           (search-path-specification
-            (variable "LIBRARY_PATH")
-            (files '("lib" "lib64")))))))
+       ,@(package-inputs gcc-4.7)))))
 
 (define-public gcc-7
   (package
diff --git a/guix/build-system/gnu.scm b/guix/build-system/gnu.scm
index 3cc89f8852..6e66f5ffce 100644
--- a/guix/build-system/gnu.scm
+++ b/guix/build-system/gnu.scm
@@ -1,5 +1,5 @@
 ;;; GNU Guix --- Functional package management for GNU
-;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2019 Ludovic Courtès <ludo@gnu.org>
+;;; Copyright © 2012, 2013, 2014, 2015, 2016, 2017, 2019, 2020 Ludovic Courtès <ludo@gnu.org>
 ;;;
 ;;; This file is part of GNU Guix.
 ;;;
@@ -296,13 +296,19 @@ standard packages used as implicit inputs of the GNU build system."
                           `(("source" ,source))
                           '())
                     ,@native-inputs
+
+                    ;; When not cross-compiling, ensure implicit inputs come
+                    ;; last.  That way, libc headers come last, which allows
+                    ;; #include_next to work correctly; see
+                    ;; <https://bugs.gnu.org/30756>.
+                    ,@(if target '() inputs)
                     ,@(if (and target implicit-cross-inputs?)
                           (standard-cross-packages target 'host)
                           '())
                     ,@(if implicit-inputs?
                           (standard-packages)
                           '())))
-    (host-inputs inputs)
+    (host-inputs (if target inputs '()))
 
     ;; The cross-libc is really a target package, but for bootstrapping
     ;; reasons, we can't put it in 'host-inputs'.  Namely, 'cross-gcc' is a