diff --git a/gnu/packages/base.scm b/gnu/packages/base.scm
index f048e4b1194..d74d304de14 100644
--- a/gnu/packages/base.scm
+++ b/gnu/packages/base.scm
@@ -6,7 +6,7 @@
 ;;; Copyright © 2014 Alex Kost <alezost@gmail.com>
 ;;; Copyright © 2014, 2015 Manolis Fragkiskos Ragkousis <manolis837@gmail.com>
 ;;; Copyright © 2016, 2017, 2019, 2020 Efraim Flashner <efraim@flashner.co.il>
-;;; Copyright © 2016 Jan Nieuwenhuizen <janneke@gnu.org>
+;;; Copyright © 2016, 2020 Jan (janneke) Nieuwenhuizen <janneke@gnu.org>
 ;;; Copyright © 2016, 2018 Alex Vong <alexvong1995@gmail.com>
 ;;; Copyright © 2017 Rene Saavedra <rennes@openmailbox.org>
 ;;; Copyright © 2017, 2020 Mathieu Othacehe <m.othacehe@gmail.com>
@@ -303,11 +303,13 @@ used to apply commands with arbitrarily long arguments.")
    (inputs `(("acl"  ,acl)                        ; TODO: add SELinux
              ("gmp"  ,gmp)                        ;bignums in 'expr', yay!
 
-             ;; Drop the dependency on libcap when cross-compiling since it's
-             ;; not quite cross-compilable.
-             ,@(if (%current-target-system)
-                   '()
-                   `(("libcap" ,libcap)))))  ;capability support is 'ls', etc.
+             ;; Do not use libcap when cross-compiling since it's not quite
+             ;; cross-compilable; and use it only for supported systems.
+             ,@(if (and (not (%current-target-system))
+                        (not (member (%current-system)
+                                     (package-supported-systems libcap))))
+             `(("libcap" ,libcap))  ;capability support in 'ls', etc.
+             '())))
    (native-inputs
     ;; Perl is needed to run tests in native builds, and to run the bundled
     ;; copy of help2man.  However, don't pass it when cross-compiling since
diff --git a/gnu/packages/linux.scm b/gnu/packages/linux.scm
index e9f261e859f..977f448b56c 100644
--- a/gnu/packages/linux.scm
+++ b/gnu/packages/linux.scm
@@ -42,6 +42,7 @@
 ;;; Copyright © 2020 Pierre Neidhardt <mail@ambrevar.xyz>
 ;;; Copyright © 2020 Chris Marusich <cmmarusich@gmail.com>
 ;;; Copyright © 2020 Vincent Legoll <vincent.legoll@gmail.com>
+;;; Copyright © 2020 Jan (janneke) Nieuwenhuizen <janneke@gnu.org>
 ;;;
 ;;; This file is part of GNU Guix.
 ;;;
@@ -2068,6 +2069,7 @@ configuration (iptunnel, ipmaddr).")
                                                    (assoc-ref %outputs "out"))
                                     "RAISE_SETFCAP=no")))
     (native-inputs `(("perl" ,perl)))
+    (supported-systems (delete "i586-gnu" %supported-systems))
     (home-page "https://sites.google.com/site/fullycapable/")
     (synopsis "Library for working with POSIX capabilities")
     (description