diff --git a/swh/deposit/tests/api/test_checks.py b/swh/deposit/tests/api/test_checks.py
--- a/swh/deposit/tests/api/test_checks.py
+++ b/swh/deposit/tests/api/test_checks.py
@@ -162,6 +162,38 @@
             </entry>
             """,
         ),
+        (
+            "codemeta-date-month",
+            # Allowed by ISO8601, therefore by schema:Date, but not by xsd:date
+            f"""\
+            <entry {XMLNS}>
+                <url>some url</url>
+                <external_identifier>some id</external_identifier>
+                <name>nar</name>
+                <author>no one</author>
+                <codemeta:datePublished>2020-12</codemeta:datePublished>
+                <codemeta:dateCreated>2020-12</codemeta:dateCreated>
+                <codemeta:dateModified>2020-12</codemeta:dateModified>
+                {PROVENANCE_XML}
+            </entry>
+            """,
+        ),
+        (
+            "codemeta-date-year",
+            # Allowed by ISO8601, therefore by schema:Date, but not by xsd:date
+            f"""\
+            <entry {XMLNS}>
+                <url>some url</url>
+                <external_identifier>some id</external_identifier>
+                <name>nar</name>
+                <author>no one</author>
+                <codemeta:datePublished>2020</codemeta:datePublished>
+                <codemeta:dateCreated>2020</codemeta:dateCreated>
+                <codemeta:dateModified>2020</codemeta:dateModified>
+                {PROVENANCE_XML}
+            </entry>
+            """,
+        ),
         (
             "codemeta-datetimes",
             # technically, only Date is allowed for datePublished; but we allow DateTime
diff --git a/swh/deposit/xsd/codemeta.xsd b/swh/deposit/xsd/codemeta.xsd
--- a/swh/deposit/xsd/codemeta.xsd
+++ b/swh/deposit/xsd/codemeta.xsd
@@ -16,8 +16,18 @@
   <xsd:element name="dateModified" type="codemeta:DateOrDateTime" />
   <xsd:element name="embargoDate" type="xsd:date" />
 
+  <xsd:simpleType name="Date">
+    <!-- schema:Date allows truncated formats, but XML Schema primitive types
+         need to be joined to approximate it:
+         https://www.w3.org/TR/xmlschema-2/#truncatedformats
+         Note that this is stricter than ISO8601. For example, it does not
+         allow week dates or ordinal days.
+      -->
+    <xsd:union memberTypes="xsd:date xsd:gYearMonth xsd:gYear"/>
+  </xsd:simpleType>
+
   <xsd:simpleType name="DateOrDateTime">
-    <xsd:union memberTypes="xsd:date xsd:dateTime"/>
+    <xsd:union memberTypes="codemeta:Date xsd:dateTime"/>
   </xsd:simpleType>
 
   <xsd:element name="author" type="codemeta:PersonOrOrganization" />