diff --git a/.github/workflows/ci.ml b/.github/workflows/ci.ml
index 55808f635b1..e628ac7999e 100644
--- a/.github/workflows/ci.ml
+++ b/.github/workflows/ci.ml
@@ -472,7 +472,7 @@ let main oc : unit =
     (* These should be identical to the values in appveyor.yml *)
     ("OPAM_REPO", "https://github.com/ocaml/opam-repository.git");
     ("OPAM_TEST_REPO_SHA", "dff745994c64d083a6ba3ddc5a9c28ed0ad0f40a");
-    ("OPAM_REPO_SHA", "dff745994c64d083a6ba3ddc5a9c28ed0ad0f40a");
+    ("OPAM_REPO_SHA", "6eee105e52e098e36949a584c053a18bcb9b2f6b");
     ("SOLVER", "");
     (* Cygwin configuration *)
     ("CYGWIN_MIRROR", "http://mirrors.kernel.org/sourceware/cygwin/");
diff --git a/.github/workflows/depexts.yml b/.github/workflows/depexts.yml
index 7dcbcc1d9c5..88355bd2f5b 100644
--- a/.github/workflows/depexts.yml
+++ b/.github/workflows/depexts.yml
@@ -18,7 +18,7 @@ defaults:
 env:
   OPAMVERSION: 2.1.6
   OPAM_REPO: https://github.com/ocaml/opam-repository.git
-  OPAM_REPO_SHA: dff745994c64d083a6ba3ddc5a9c28ed0ad0f40a
+  OPAM_REPO_SHA: 6eee105e52e098e36949a584c053a18bcb9b2f6b
 
 jobs:
   opam-cache:
diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 4d7d9624140..87567fa4a5e 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -27,7 +27,7 @@ env:
   OPAM12CACHE: ~/.cache/opam1.2/cache
   OPAM_REPO: https://github.com/ocaml/opam-repository.git
   OPAM_TEST_REPO_SHA: dff745994c64d083a6ba3ddc5a9c28ed0ad0f40a
-  OPAM_REPO_SHA: dff745994c64d083a6ba3ddc5a9c28ed0ad0f40a
+  OPAM_REPO_SHA: 6eee105e52e098e36949a584c053a18bcb9b2f6b
   SOLVER:
   CYGWIN_MIRROR: http://mirrors.kernel.org/sourceware/cygwin/
   CYGWIN_ROOT: D:\cygwin
diff --git a/configure b/configure
index 6a916830055..b4f27953b88 100755
--- a/configure
+++ b/configure
@@ -6594,8 +6594,8 @@ printf "%s\n" "not found" >&6; }
 
 
 
-  { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for OCaml findlib package opam-0install-cudf 0.4 or later" >&5
-printf %s "checking for OCaml findlib package opam-0install-cudf 0.4 or later... " >&6; }
+  { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for OCaml findlib package opam-0install-cudf 0.5.0 or later" >&5
+printf %s "checking for OCaml findlib package opam-0install-cudf 0.5.0 or later... " >&6; }
 
   if version=`$OCAMLFIND query opam-0install-cudf -format '%v' 2>/dev/null`
 then :
@@ -6619,7 +6619,7 @@ then :
                      -e 's/[^0-9]//g'`
 
 
-  ax_compare_version_B=`echo "0.4" | sed -e 's/\([0-9]*\)/Z\1Z/g' \
+  ax_compare_version_B=`echo "0.5.0" | sed -e 's/\([0-9]*\)/Z\1Z/g' \
                      -e 's/Z\([0-9]\)Z/Z0\1Z/g' \
                      -e 's/Z\([0-9][0-9]\)Z/Z0\1Z/g' \
                      -e 's/Z\([0-9][0-9][0-9]\)Z/Z0\1Z/g' \
diff --git a/configure.ac b/configure.ac
index 1dd909807d4..b8eee9723cc 100644
--- a/configure.ac
+++ b/configure.ac
@@ -376,7 +376,7 @@ AC_CHECK_OCAML_PKG_AT_LEAST([dose3.common], [6.1])
 AC_CHECK_OCAML_PKG_AT_LEAST([dose3.algo], [6.1])
 AC_CHECK_OCAML_PKG_AT_LEAST([opam-file-format], [2.1.4])
 AC_CHECK_OCAML_PKG([spdx_licenses])
-AC_CHECK_OCAML_PKG_AT_LEAST([opam-0install-cudf],[0.4])
+AC_CHECK_OCAML_PKG_AT_LEAST([opam-0install-cudf],[0.5.0])
 AC_CHECK_OCAML_PKG([jsonm])
 AC_CHECK_OCAML_PKG([uutf])
 AC_CHECK_OCAML_PKG([sha])
diff --git a/master_changes.md b/master_changes.md
index 73bb678f71d..90369d5c2f7 100644
--- a/master_changes.md
+++ b/master_changes.md
@@ -94,6 +94,8 @@ users)
 ## Build
  * Synchronise opam-core.opam with opam-repository changes [#6043 @dra27]
   * Unset OPAM_SWITCH_PREFIX when using make cold [#5534 @kit-ty-kate]
+  * Bump the vendored opam-0install-cudf to 0.5.0 [#6130 @kit-ty-kate]
+  * Require opam-0install-cudf >= 0.5.0 [#6130 @kit-ty-kate]
 
 ## Infrastructure
 
@@ -121,6 +123,11 @@ users)
 ## Opam file format
 
 ## Solver
+  * Add support for unordered criteria with the `builtin-0install` solver [#6130 @kit-ty-kate]
+  * Add support for the `-changed` criteria with the `builtin-0install` solver, to make the solver prefer to keep packages installed at their current version [#6130 @kit-ty-kate]
+  * Add support for the `-count[avoid-version,solution]` criteria with the `builtin-0install` solver, to avoid packages marked with `avoid-version` flag [#6130 @kit-ty-kate]
+  * The default criteria for the `builtin-0install` solver changed from empty to `-changed,-count[avoid-version,solution]` [#6130 @kit-ty-kate]
+  * The upgrade and fixup criteria for the `builtin-0install` solver changed from empty to `-count[avoid-version,solution]` [#6130 @kit-ty-kate]
 
 ## Client
 
diff --git a/opam-solver.opam b/opam-solver.opam
index 7a15dbef61c..40ead91ed5c 100644
--- a/opam-solver.opam
+++ b/opam-solver.opam
@@ -35,7 +35,7 @@ depends: [
   "cudf" {>= "0.7"}
   "re" {>= "1.9.0"}
   "dune" {>= "2.0.0"}
-  "opam-0install-cudf" {>= "0.4"}
+  "opam-0install-cudf" {>= "0.5.0"}
 ]
 depopts: [
   "z3"
diff --git a/src/solver/opamBuiltin0install.ml b/src/solver/opamBuiltin0install.ml
index bc5c9c3fa37..3c672a760a0 100644
--- a/src/solver/opamBuiltin0install.ml
+++ b/src/solver/opamBuiltin0install.ml
@@ -23,9 +23,10 @@ let command_name = None
 let preemptive_check = false
 
 let default_criteria = {
-  crit_default = "";
-  crit_upgrade = "";
-  crit_fixup = "";
+  crit_default = "-changed,\
+                  -count[avoid-version,solution]";
+  crit_upgrade = "-count[avoid-version,solution]";
+  crit_fixup = "-count[avoid-version,solution]";
   crit_best_effort_prefix = None;
 }
 
@@ -90,25 +91,54 @@ let reconstruct_universe universe selections =
 type options = {
   drop_installed_packages : bool;
   prefer_oldest : bool;
+  handle_avoid_version : bool;
+  prefer_installed : bool;
 }
 
 let parse_criteria criteria =
-  let default = {drop_installed_packages = false; prefer_oldest = false} in
-  match criteria with
-  | "" -> default
-  | "+removed" -> {drop_installed_packages = true; prefer_oldest = false}
-  | "+count[version-lag,solution]" -> {drop_installed_packages = false; prefer_oldest = true}
-  | "+removed,+count[version-lag,solution]" ->
-    {drop_installed_packages = true; prefer_oldest = true}
-  | _ ->
-    OpamConsole.warning "Criteria '%s' is not supported by the 0install solver" criteria;
-    default
+  let default =
+    {
+      drop_installed_packages = false;
+      prefer_oldest = false;
+      handle_avoid_version = false;
+      prefer_installed = false;
+    }
+  in
+  let rec parse default (criteria : OpamCudfCriteria.criterion list) =
+    match criteria with
+    | [] -> default
+    | (Plus, Removed, None)::xs ->
+      parse {default with drop_installed_packages = true} xs
+    | (Plus, Solution, Some "version-lag")::xs ->
+      parse {default with prefer_oldest = true} xs
+    | (Minus, Solution, Some "avoid-version")::xs ->
+      parse {default with handle_avoid_version = true} xs
+    | (Minus, Changed, None)::xs ->
+      parse {default with prefer_installed = true} xs
+    | criterion::xs ->
+      OpamConsole.warning
+        "Criteria '%s' is not supported by the 0install solver"
+        (OpamCudfCriteria.criterion_to_string criterion);
+      parse default xs
+  in
+  parse default (OpamCudfCriteria.of_string criteria)
 
 let call ~criteria ?timeout:_ (preamble, universe, request) =
-  let {drop_installed_packages; prefer_oldest} = parse_criteria criteria in
+  let {
+    drop_installed_packages;
+    prefer_oldest;
+    handle_avoid_version;
+    prefer_installed;
+  } =
+    parse_criteria criteria
+  in
   let timer = OpamConsole.timer () in
   let pkgs, constraints = create_spec ~drop_installed_packages universe request in
-  let context = Opam_0install_cudf.create ~prefer_oldest ~constraints universe in
+  let context =
+    Opam_0install_cudf.create
+      ~prefer_oldest ~handle_avoid_version ~prefer_installed
+      ~constraints universe
+  in
   match Opam_0install_cudf.solve context pkgs with
   | Ok selections ->
     let universe = reconstruct_universe universe selections in
diff --git a/src_ext/Makefile.sources b/src_ext/Makefile.sources
index b8079bbedb3..0bd663c1324 100644
--- a/src_ext/Makefile.sources
+++ b/src_ext/Makefile.sources
@@ -25,8 +25,8 @@ MD5_dose3 = bc99cbcea8fca29dca3ebbee54be45e1
 URL_mccs = https://github.com/ocaml-opam/ocaml-mccs/archive/refs/tags/1.1+17.tar.gz
 MD5_mccs = 844d99bc531e0713238fe4b6b8511ed1
 
-URL_opam-0install-cudf = https://github.com/ocaml-opam/opam-0install-solver/releases/download/v0.4.3/opam-0install-cudf-0.4.3.tbz
-MD5_opam-0install-cudf = ae0c197deace373ad87737468a04f76b
+URL_opam-0install-cudf = https://github.com/ocaml-opam/opam-0install-cudf/releases/download/v0.5.0/opam-0install-cudf-0.5.0.tar.gz
+MD5_opam-0install-cudf = 75419722aa839f518a25cae1b3c6efd4
 
 URL_0install-solver = https://github.com/0install/0install/releases/download/v2.18/0install-2.18.tbz
 MD5_0install-solver = 030edc9b1d3676c06d51397ffb5a737d