diff --git a/build/pkgs/flint/spkg-configure.m4 b/build/pkgs/flint/spkg-configure.m4
index ddf60b596fd..4c1a347152d 100644
--- a/build/pkgs/flint/spkg-configure.m4
+++ b/build/pkgs/flint/spkg-configure.m4
@@ -3,12 +3,12 @@ SAGE_SPKG_CONFIGURE([flint], [
         AC_CHECK_HEADER(flint/flint.h, [dnl
           dnl gr_get_fexpr appears in Flint 3.0
           AC_SEARCH_LIBS([gr_get_fexpr], [flint], [dnl
-            dnl Flint 3.1 is too new
-            AC_MSG_CHECKING([whether FLINT version is >= 3.1.0])
+            dnl Assume Flint 3.2 is too new
+            AC_MSG_CHECKING([whether FLINT version is >= 3.2.0])
             AC_COMPILE_IFELSE([dnl
               AC_LANG_PROGRAM([[#include <flint/flint.h>
-                                #if __FLINT_RELEASE >= 30100
-                                # error "FLINT 3.1 is too new"
+                                #if __FLINT_RELEASE >= 30200
+                                # error "FLINT 3.2 is too new"
                                 #endif
                               ]])
             ], [dnl
diff --git a/build/pkgs/singular/checksums.ini b/build/pkgs/singular/checksums.ini
index 40ba7b3153f..3273f5f7055 100644
--- a/build/pkgs/singular/checksums.ini
+++ b/build/pkgs/singular/checksums.ini
@@ -1,5 +1,5 @@
 tarball=singular-VERSION.tar.gz
-sha1=0dd736f26935ed72999bb9a4bbb98c6df18ab9ea
-md5=0f9368193bad9a0c3dc84545b2404761
-cksum=1698641648
-upstream_url=ftp://jim.mathematik.uni-kl.de/pub/Math/Singular/SOURCES/4-3-2/singular-VERSION.tar.gz
+sha1=1f678e1cc756fd8dc29dcdef5ae67441b6bcc779
+md5=09382cdacbfe67b4099056b65c2ec016
+cksum=244065751
+upstream_url=ftp://jim.mathematik.uni-kl.de/pub/Math/Singular/SOURCES/${VERSION_MAJOR}-${VERSION_MINOR}-${VERSION_MICRO}/singular-VERSION.tar.gz
diff --git a/build/pkgs/singular/package-version.txt b/build/pkgs/singular/package-version.txt
index 7801ff9a882..fdc6698807a 100644
--- a/build/pkgs/singular/package-version.txt
+++ b/build/pkgs/singular/package-version.txt
@@ -1 +1 @@
-4.3.2p8
+4.4.0