diff --git a/format-specs/geoparquet.md b/format-specs/geoparquet.md
index dc5324e..d476139 100644
--- a/format-specs/geoparquet.md
+++ b/format-specs/geoparquet.md
@@ -227,7 +227,7 @@ Note: This technique to use the bounding box to improve spatial queries does not
 
 ### Bounding Box Columns
 
-A bounding box column MUST be a Parquet group field with 4 child fields named `xmin`, `xmax`, `ymin`, and `ymax` representing the geometry's coordinate range. As with the top-level [`bbox`](#bbox) column, the values follow the GeoJSON specification (RFC 7946, section 5), which also describes how to represent the bbox for geometries that cross the antimeridian. For three dimensions the additional fields `zmin` and `zmax` MAY be present but are not required. The fields MUST be of Parquet type `FLOAT` or `DOUBLE` and all columns MUST use the same type. The repetition of a bounding box column MUST match the geometry column's [repetition](#repetition). A row MUST contain a bounding box value if and only if the row contains a geometry value. In cases where the geometry is optional and a row does not contain a geometry value, the row MUST NOT contain a bounding box value.
+A bounding box column MUST be a Parquet group field with 4 or 6 child fields representing the geometry's coordinate range. For two-dimensional data, the child fields MUST be named `xmin`, `ymin`, `xmax`, and `ymax` and MUST be ordered in this same way. As with the top-level [`bbox`](#bbox) column, the values follow the GeoJSON specification (RFC 7946, section 5), which also describes how to represent the bbox for geometries that cross the antimeridian. For three dimensions the additional fields `zmin` and `zmax` MAY be present but are not required. If `zmin` is present then `zmax` MUST be present and vice versa. If `zmin` and `zmax` are present, the ordering of the child fields MUST be `xmin`, `ymin`, `zmin`, `xmax`, `ymax`, `zmax`. The fields MUST be of Parquet type `FLOAT` or `DOUBLE` and all columns MUST use the same type. The repetition of a bounding box column MUST match the geometry column's [repetition](#repetition). A row MUST contain a bounding box value if and only if the row contains a geometry value. In cases where the geometry is optional and a row does not contain a geometry value, the row MUST NOT contain a bounding box value.
 
 The bounding box column MUST be at the root of the schema. The bounding box column MUST NOT be nested in a group.
 
diff --git a/format-specs/schema.json b/format-specs/schema.json
index 7db7ab0..26cddec 100644
--- a/format-specs/schema.json
+++ b/format-specs/schema.json
@@ -74,7 +74,9 @@
             },
             "covering": {
               "type": "object",
-              "minProperties": 1,
+              "required": [
+                "bbox"
+              ],
               "properties": {
                 "bbox": {
                   "type": "object",
@@ -83,7 +85,7 @@
                     "xmin": {
                       "type": "array",
                       "items": [
-                        { "type": "string" },
+                        { "type": "string", "minLength": 1 },
                         { "const": "xmin" }
                       ],
                       "minItems": 2,
@@ -92,7 +94,7 @@
                     "xmax": {
                       "type": "array",
                       "items": [
-                        { "type": "string" },
+                        { "type": "string", "minLength": 1 },
                         { "const": "xmax" }
                       ],
                       "minItems": 2,
@@ -101,7 +103,7 @@
                     "ymin": {
                       "type": "array",
                       "items": [
-                        { "type": "string" },
+                        { "type": "string", "minLength": 1 },
                         { "const": "ymin" }
                       ],
                       "minItems": 2,
@@ -110,7 +112,7 @@
                     "ymax": {
                       "type": "array",
                       "items": [
-                        { "type": "string" },
+                        { "type": "string", "minLength": 1 },
                         { "const": "ymax" }
                       ],
                       "minItems": 2,
diff --git a/scripts/test_json_schema.py b/scripts/test_json_schema.py
index be0888f..61a1b4b 100644
--- a/scripts/test_json_schema.py
+++ b/scripts/test_json_schema.py
@@ -221,7 +221,6 @@ def get_version() -> str:
     },
 }
 
-
 # Allow "any_column.xmin" etc.
 metadata = copy.deepcopy(metadata_covering_template)
 valid_cases["valid_default_bbox"] = metadata
@@ -235,6 +234,15 @@ def get_version() -> str:
 }
 valid_cases["valid_but_not_bbox_struct_name"] = metadata
 
+metadata = copy.deepcopy(metadata_covering_template)
+metadata["columns"]["geometry"]["covering"]["bbox"] = {
+    "xmin": ["", "xmin"],
+    "ymin": ["", "ymin"],
+    "xmax": ["", "xmax"],
+    "ymax": ["", "ymax"],
+}
+invalid_cases["empty_column_name"] = metadata
+
 metadata = copy.deepcopy(metadata_covering_template)
 metadata["columns"]["geometry"]["covering"]["bbox"]["xmin"] = []
 invalid_cases["xmin_array_length_must_be_2_is_0"] = metadata