diff --git a/src/Microsoft.ML.Data/Scorers/BinaryClassifierScorer.cs b/src/Microsoft.ML.Data/Scorers/BinaryClassifierScorer.cs
index 2bfa94ffd8..4ddf832782 100644
--- a/src/Microsoft.ML.Data/Scorers/BinaryClassifierScorer.cs
+++ b/src/Microsoft.ML.Data/Scorers/BinaryClassifierScorer.cs
@@ -187,9 +187,6 @@ private protected override void SaveAsOnnxCore(OnnxContext ctx)
             Host.Assert(Bindable is IBindableCanSaveOnnx);
             Host.Assert(Bindings.InfoCount >= 2);
 
-            if (!ctx.ContainsColumn(DefaultColumnNames.Features))
-                return;
-
             base.SaveAsOnnxCore(ctx);
             int delta = Bindings.DerivedColumnCount;
 
diff --git a/test/Microsoft.ML.Tests/OnnxConversionTest.cs b/test/Microsoft.ML.Tests/OnnxConversionTest.cs
index 9f2482961f..c14637e745 100644
--- a/test/Microsoft.ML.Tests/OnnxConversionTest.cs
+++ b/test/Microsoft.ML.Tests/OnnxConversionTest.cs
@@ -1959,6 +1959,144 @@ public void SelectColumnsOnnxTest()
             Done();
         }
 
+        private class BreastCancerMulticlassExampleNonDefaultColNames
+        {
+            [LoadColumn(1)]
+            public string Label;
+
+            [LoadColumn(2, 9), VectorType(8)]
+            public float[] MyFeatureVector;
+        }
+
+        private class BreastCancerBinaryClassificationNonDefaultColNames
+        {
+            [LoadColumn(0)]
+            public bool Label;
+
+            [LoadColumn(2, 9), VectorType(8)]
+            public float[] MyFeatureVector;
+        }
+
+        [Fact]
+        public void NonDefaultColNamesBinaryClassificationOnnxConversionTest()
+        {
+            var mlContext = new MLContext(seed: 1);
+            string dataPath = GetDataPath("breast-cancer.txt");
+            // Now read the file (remember though, readers are lazy, so the actual reading will happen when the data is accessed).
+            var dataView = mlContext.Data.LoadFromTextFile<BreastCancerBinaryClassificationNonDefaultColNames>(dataPath, separatorChar: '\t', hasHeader: true);
+            List<IEstimator<ITransformer>> estimators = new List<IEstimator<ITransformer>>()
+            {
+                mlContext.BinaryClassification.Trainers.AveragedPerceptron("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.FastForest("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.FastTree("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.LbfgsLogisticRegression("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.LinearSvm("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.Prior(),
+                mlContext.BinaryClassification.Trainers.SdcaLogisticRegression("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.SdcaNonCalibrated("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.SgdCalibrated("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.SgdNonCalibrated("Label", "MyFeatureVector"),
+                mlContext.BinaryClassification.Trainers.SymbolicSgdLogisticRegression("Label", "MyFeatureVector"),
+            };
+            if (Environment.Is64BitProcess)
+            {
+                estimators.Add(mlContext.BinaryClassification.Trainers.LightGbm("Label", "MyFeatureVector"));
+            }
+
+            var initialPipeline = mlContext.Transforms.ReplaceMissingValues("MyFeatureVector").
+                Append(mlContext.Transforms.NormalizeMinMax("MyFeatureVector"));
+            foreach (var estimator in estimators)
+            {
+                var pipeline = initialPipeline.Append(estimator);
+                var model = pipeline.Fit(dataView);
+                var transformedData = model.Transform(dataView);
+                var onnxModel = mlContext.Model.ConvertToOnnxProtobuf(model, dataView);
+
+                var onnxFileName = $"{estimator.ToString()}.onnx";
+                var onnxModelPath = GetOutputPath(onnxFileName);
+                SaveOnnxModel(onnxModel, onnxModelPath, null);
+
+                // Compare model scores produced by ML.NET and ONNX's runtime.
+                if (IsOnnxRuntimeSupported())
+                {
+                    // Evaluate the saved ONNX model using the data used to train the ML.NET pipeline.
+                    var onnxEstimator = mlContext.Transforms.ApplyOnnxModel(onnxModelPath);
+                    var onnxTransformer = onnxEstimator.Fit(dataView);
+                    var onnxResult = onnxTransformer.Transform(dataView);
+                    CompareSelectedColumns<float>("Score", "Score", transformedData, onnxResult, 3); //compare scores
+                    CompareSelectedColumns<bool>("PredictedLabel", "PredictedLabel", transformedData, onnxResult); //compare predicted labels
+                }
+            }
+            Done();
+        }
+
+        [Fact]
+        public void NonDefaultColNamesMultiClassificationOnnxConversionTest()
+        {
+            var mlContext = new MLContext(seed: 1);
+
+            string dataPath = GetDataPath("breast-cancer.txt");
+            var dataView = mlContext.Data.LoadFromTextFile<BreastCancerMulticlassExampleNonDefaultColNames>(dataPath, separatorChar: '\t', hasHeader: true);
+
+            List<IEstimator<ITransformer>> estimators = new List<IEstimator<ITransformer>>()
+            {
+                mlContext.MulticlassClassification.Trainers.LbfgsMaximumEntropy("Label", "MyFeatureVector"),
+                mlContext.MulticlassClassification.Trainers.NaiveBayes("Label", "MyFeatureVector"),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.AveragedPerceptron("Label", "MyFeatureVector")),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.AveragedPerceptron("Label", "MyFeatureVector"), useProbabilities:false),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.LbfgsLogisticRegression("Label", "MyFeatureVector")),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.LbfgsLogisticRegression("Label", "MyFeatureVector"), useProbabilities:false),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.LinearSvm("Label", "MyFeatureVector")),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.LinearSvm("Label", "MyFeatureVector"), useProbabilities:false),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.FastForest("Label", "MyFeatureVector")),
+                mlContext.MulticlassClassification.Trainers.OneVersusAll(
+                    mlContext.BinaryClassification.Trainers.FastForest("Label", "MyFeatureVector"), useProbabilities:false),
+                mlContext.MulticlassClassification.Trainers.SdcaMaximumEntropy("Label", "MyFeatureVector"),
+                mlContext.MulticlassClassification.Trainers.SdcaNonCalibrated("Label", "MyFeatureVector")
+            };
+
+            if (Environment.Is64BitProcess)
+            {
+                estimators.Add(mlContext.MulticlassClassification.Trainers.LightGbm("Label", "MyFeatureVector"));
+            }
+
+            var initialPipeline = mlContext.Transforms.ReplaceMissingValues("MyFeatureVector")
+                .Append(mlContext.Transforms.NormalizeMinMax("MyFeatureVector"))
+                .Append(mlContext.Transforms.Conversion.MapValueToKey("Label"));
+
+            foreach (var estimator in estimators)
+            {
+                var pipeline = initialPipeline.Append(estimator);
+                var model = pipeline.Fit(dataView);
+                var transformedData = model.Transform(dataView);
+
+                var onnxModel = mlContext.Model.ConvertToOnnxProtobuf(model, dataView);
+                var onnxFileName = $"{estimator.ToString()}.onnx";
+                var onnxModelPath = GetOutputPath(onnxFileName);
+
+                SaveOnnxModel(onnxModel, onnxModelPath, null);
+
+                // Compare results produced by ML.NET and ONNX's runtime.
+                if (IsOnnxRuntimeSupported())
+                {
+                    // Evaluate the saved ONNX model using the data used to train the ML.NET pipeline.
+                    var onnxEstimator = mlContext.Transforms.ApplyOnnxModel(onnxModelPath);
+                    var onnxTransformer = onnxEstimator.Fit(dataView);
+                    var onnxResult = onnxTransformer.Transform(dataView);
+                    CompareSelectedColumns<uint>("PredictedLabel", "PredictedLabel", transformedData, onnxResult);
+                    CompareSelectedColumns<float>("Score", "Score", transformedData, onnxResult, 4);
+                }
+            }
+            Done();
+        }
+
         private void CompareResults(string leftColumnName, string rightColumnName, IDataView left, IDataView right, int precision = 6)
         {
             var leftColumn = left.Schema[leftColumnName];