diff --git a/baselibs.conf b/baselibs.conf
index 0a969f9..2ebdeed 100644
--- a/baselibs.conf
+++ b/baselibs.conf
@@ -1,4 +1,19 @@
-strace
-  +/usr/bin/strace-graph -> /usr/bin/strace-graph<extension>
-  +/usr/bin/strace -> /usr/bin/strace<extension>
-  prereq -glibc-x86
+# strace.{x86_64,sparc64,ppc64,...} can already trace both ELF32 and ELF64
+# processes, and there is no need for having an strace32.
+#
+# Using baselibs, we could create a strace-64bit.ppc/strace-64bit.sparc
+# convenience package (for systems with mostly-ELF32 userspace), but then
+# again, one can just as well install strace.ppc64 to get the same effect…
+#
+arch ppc64 package strace
+	+/usr/bin/strace-graph -> /usr/bin/strace-graph<extension>
+	+/usr/bin/strace -> /usr/bin/strace<extension>
+
+
+# IA64 oddball: it uses that special kind of emulation, so in this case,
+# the strace-x86 may still be needed!
+#
+arch ia64 package strace
+	+/usr/bin/strace-graph -> /usr/bin/strace-graph<extension>
+	+/usr/bin/strace -> /usr/bin/strace<extension>
+	prereq -glibc-x86
diff --git a/strace.changes b/strace.changes
index a95d4dc..230191f 100644
--- a/strace.changes
+++ b/strace.changes
@@ -1,3 +1,9 @@
+-------------------------------------------------------------------
+Sun Mar 29 17:02:23 UTC 2015 - jengelh@inai.de
+
+- Drop strace-32bit, since the normal strace build is powerful
+  enough. [bnc#924827]
+
 -------------------------------------------------------------------
 Tue Mar 24 09:02:49 UTC 2015 - schwab@suse.de
 
diff --git a/strace.spec b/strace.spec
index 6ac1ba3..93bec2c 100644
--- a/strace.spec
+++ b/strace.spec
@@ -57,6 +57,9 @@ BuildRequires:  xz
 %ifarch ppc64
 Obsoletes:      strace-64bit
 %endif
+%ifarch x86_64
+Obsoletes:      strace-32bit
+%endif
 
 %description
 With strace, you can trace the activity of a program.  Information