diff --git a/perl-AnyEvent.spec b/perl-AnyEvent.spec
index d5195c2..af9cc11 100644
--- a/perl-AnyEvent.spec
+++ b/perl-AnyEvent.spec
@@ -3,9 +3,15 @@
 # A noarch-turned-arch package should not have debuginfo
 %global debug_package %{nil}
 
+# Use weak dependencies where available
+%global have_weak_deps 0%{?fedora} > 20 || 0%{?rhel} > 7
+
+# SSL in Rawhide is currently flaky, probably due to pulling in a mix of OpenSSL versions
+%global flaky_ssl 0%{?fedora} == 26
+
 Name:           perl-AnyEvent
 Version:        7.13
-Release:        1%{?dist}
+Release:        2%{?dist}
 Summary:        Framework for multiple event loops
 Group:          Development/Libraries
 License:        GPL+ or Artistic
@@ -23,22 +29,35 @@ BuildRequires:  perl(ExtUtils::MakeMaker)
 
 # Module requirements
 BuildRequires:  perl >= 3:5.8.1
+BuildRequires:  perl(B)
 BuildRequires:  perl(base)
 BuildRequires:  perl(Carp)
+BuildRequires:  perl(Errno)
 BuildRequires:  perl(Exporter)
+BuildRequires:  perl(File::Temp)
+BuildRequires:  perl(Guard)
+BuildRequires:  perl(integer)
+BuildRequires:  perl(JSON::XS)
 BuildRequires:  perl(List::Util)
 BuildRequires:  perl(overload)
+BuildRequires:  perl(POSIX)
 BuildRequires:  perl(Scalar::Util)
 BuildRequires:  perl(Socket)
 BuildRequires:  perl(Storable)
+BuildRequires:  perl(strict)
+BuildRequires:  perl(Sys::Syslog)
 BuildRequires:  perl(Task::Weaken)
 BuildRequires:  perl(Time::HiRes)
+BuildRequires:  perl(Unicode::Normalize)
 
 # Test suite requirements
 BuildRequires:  perl(File::Spec)
-BuildRequires:  perl(File::Temp)
-BuildRequires:  perl(Net::SSLeay)
+%if !(%flaky_ssl)
+BuildRequires:  perl(Net::SSLeay) >= 1.33
+%endif
 BuildRequires:  perl(Test::More)
+BuildRequires:  perl(utf8)
+BuildRequires:  perl(warnings)
 
 # Event loop testing
 #
@@ -54,8 +73,10 @@ BuildRequires:  perl(Glib) >= 1.210
 BuildRequires:  perl(POE) >= 1.312
 BuildRequires:  perl(Tk)
 %if 0%{?fedora}
+%if !(%flaky_ssl)
 BuildRequires:  perl(AnyEvent::AIO)
-BuildRequires:  perl(EV)
+%endif
+BuildRequires:  perl(EV) >= 4.00
 BuildRequires:  perl(IO::AIO) >= 4.13
 BuildRequires:  perl(IO::Async::Loop) >= 0.33
 %endif
@@ -63,9 +84,27 @@ BuildRequires:  perl(IO::Async::Loop) >= 0.33
 
 # Runtime requires
 Requires:       perl(:MODULE_COMPAT_%(eval "`perl -V:version`"; echo $version))
+Requires:       perl(File::Temp)
+%if %{have_weak_deps}
 # Optional but recommended
+Recommends:     perl(Guard)
+Recommends:     perl(Storable)
+Recommends:     perl(Sys::Syslog)
+Recommends:     perl(Task::Weaken)
+Recommends:     perl(Unicode::Normalize)
+# Heavier optional modules
+Suggests:       perl(CBOR::XS)
+Suggests:       perl(Coro)
+Suggests:       perl(Coro::Debug)
+Suggests:       perl(JSON::XS)
+Suggests:       perl(Net::SSLeay) >= 1.33
+%else
+Requires:       perl(Guard)
 Requires:       perl(Storable)
+Requires:       perl(Sys::Syslog)
 Requires:       perl(Task::Weaken)
+Requires:       perl(Unicode::Normalize)
+%endif
 
 # Optional dependencies we don't want to require
 %global optional_deps                  AnyEvent::AIO
@@ -161,6 +200,11 @@ make test
 
 
 %changelog
+* Mon Oct 17 2016 Paul Howarth <paul@city-fan.org> - 7.13-2
+- Add some optional dependencies (#1385642)
+- Work around SSL issues in Rawhide (possibly due to ongoing upgrade to
+  OpenSSL 1.1.0)
+
 * Mon Sep 19 2016 Paul Howarth <paul@city-fan.org> - 7.13-1
 - Update to 7.13
   - Only call tlsext_host_name for non-empty common names