diff --git a/C/Constraints/Compat.toml b/C/Constraints/Compat.toml
index 9c0b442968d91b6..abad372baf54f69 100644
--- a/C/Constraints/Compat.toml
+++ b/C/Constraints/Compat.toml
@@ -40,13 +40,18 @@ MacroTools = "0.5"
 
 ["0.4-0"]
 CompositionalNetworks = "0.5"
-ConstraintCommons = "0.1"
 PrettyTables = "2"
 julia = "1.8.0-1"
 
+["0.4-0.5.4"]
+ConstraintCommons = "0.1"
+
 ["0.5-0"]
 TestItemRunner = "0.2"
 TestItems = "0.1"
 
 ["0.5.4-0"]
 Dictionaries = "0.4"
+
+["0.5.5-0"]
+ConstraintCommons = "0.2"
diff --git a/C/Constraints/Versions.toml b/C/Constraints/Versions.toml
index dd35072c606217c..4a1db4bfb9386f5 100644
--- a/C/Constraints/Versions.toml
+++ b/C/Constraints/Versions.toml
@@ -75,3 +75,6 @@ git-tree-sha1 = "c13e8b6f4ff322c7123c2ec6ce78587d90b4c639"
 
 ["0.5.4"]
 git-tree-sha1 = "329c6428695c3e3f40ddbc0a27efe50d02eacf73"
+
+["0.5.5"]
+git-tree-sha1 = "79ffeaaf1446afacb3477daeec49e09cf523965e"