diff --git a/nomenclature/processor/region.py b/nomenclature/processor/region.py
index a30ad72d..f37b3c68 100644
--- a/nomenclature/processor/region.py
+++ b/nomenclature/processor/region.py
@@ -323,7 +323,7 @@ def apply(self, df: IamDataFrame, dsd: DataStructureDefinition) -> IamDataFrame:
 
             # If no mapping is defined the data frame is returned unchanged
             if model not in self.mappings:
-                logger.info(f"No region aggregation mapping found for model {model}")
+                logger.info(f"No model mapping found for model {model}")
                 processed_dfs.append(model_df)
 
             # Otherwise we first rename, then aggregate
@@ -331,7 +331,7 @@ def apply(self, df: IamDataFrame, dsd: DataStructureDefinition) -> IamDataFrame:
                 # before aggregating, check that all regions are valid
                 self.mappings[model].validate_regions(dsd)
                 logger.info(
-                    f"Applying region aggregation for model {model} from file "
+                    f"Applying region-processing for model {model} from file "
                     f"{self.mappings[model].file}"
                 )
 
@@ -408,7 +408,8 @@ def apply(self, df: IamDataFrame, dsd: DataStructureDefinition) -> IamDataFrame:
 
         if not processed_dfs:
             raise ValueError(
-                f"The region aggregation for model {model} resulted in an empty dataset"
+                f"The region-processing for model(s) {df.model} returned an empty "
+                "dataset"
             )
 
         return pyam.concat(processed_dfs)
diff --git a/tests/data/region_processing/rename_only/rename_only.yaml b/tests/data/region_processing/rename_only/model_a.yaml
similarity index 100%
rename from tests/data/region_processing/rename_only/rename_only.yaml
rename to tests/data/region_processing/rename_only/model_a.yaml
diff --git a/tests/data/region_processing/rename_only/model_b.yaml b/tests/data/region_processing/rename_only/model_b.yaml
new file mode 100644
index 00000000..79b3795f
--- /dev/null
+++ b/tests/data/region_processing/rename_only/model_b.yaml
@@ -0,0 +1,4 @@
+model: model_b
+native_regions:
+  - region_a: region_A
+  - region_B
diff --git a/tests/test_core.py b/tests/test_core.py
index cb85a8bf..8dc3830e 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -55,12 +55,12 @@ def test_region_processing_empty_raises():
         pd.DataFrame(
             [
                 ["model_a", "scen_a", "region_foo", "Primary Energy", "EJ/yr", 1, 2],
+                ["model_b", "scen_a", "region_foo", "Primary Energy", "EJ/yr", 1, 2],
             ],
             columns=IAMC_IDX + [2005, 2010],
         )
     )
-
-    with pytest.raises(ValueError, match="The region aggregation for model model_a"):
+    with pytest.raises(ValueError, match=("'model_a', 'model_b'.*empty dataset")):
         process(
             test_df,
             DataStructureDefinition(TEST_DATA_DIR / "region_processing/dsd"),