diff --git a/examples/synthetic_api_example/run_synthetic_rve.py b/examples/synthetic_api_example/run_synthetic_rve.py
index 086c18b..035e39a 100644
--- a/examples/synthetic_api_example/run_synthetic_rve.py
+++ b/examples/synthetic_api_example/run_synthetic_rve.py
@@ -40,6 +40,7 @@
 MELT_POOL_HEIGHT = 30.0e-6
 MELT_POOL_WIDTH_STD_DEV = 18.0e-6
 MELT_POOL_LENGTH = 300.0e-6
+N_MODES = 50
 
 HEIGHT_SHAPE_FACTOR = 1.0
 DEPTH_SHAPE_FACTOR = 1.0
@@ -99,16 +100,16 @@ def build_melt_pool():
 
     # assign shape to melt pool and cap (1 = parabola, 2 = ellipse)
     melt_pool_dict = {
-        "width": (width_data, None, 1.0, 2.0),
+        "width": (width_data, N_MODES, 1.0, 2.0),
         "depth": (
             width_data,
-            None,
+            N_MODES,
             depth_scale,
             DEPTH_SHAPE_FACTOR,
         ),
         "height": (
             width_data,
-            None,
+            N_MODES,
             height_scale,
             HEIGHT_SHAPE_FACTOR,
         ),
diff --git a/src/raptor/api.py b/src/raptor/api.py
index c6d2ead..bfc365f 100644
--- a/src/raptor/api.py
+++ b/src/raptor/api.py
@@ -9,6 +9,7 @@
 # https://github.com/ORNL-MDF/Raptor/LICENSE
 # =============================================================================
 import time
+import warnings
 from typing import Any, Dict, List, Optional
 import numpy as np
 import pandas as pd
@@ -77,18 +78,24 @@ def compute_spectral_components(
 ) -> np.ndarray:
     """Convert a uniformly sampled real signal to a sparse cosine expansion.
 
-    ``n_modes`` includes the mean (DC) mode and retains the corresponding
-    low-frequency prefix.  When ``tolerance`` is used, the smallest set of
-    Fourier bins whose discarded energy satisfies the requested reconstruction
-    RMSE is retained.
+    ``n_modes`` includes the mean (DC) mode.  By itself, it retains the
+    corresponding low-frequency prefix.  When ``tolerance`` is used, the
+    smallest set of Fourier bins whose discarded energy satisfies the requested
+    reconstruction RMSE is retained.  If both are provided, ``n_modes`` caps
+    that set while preserving its highest-energy bins; the requested tolerance
+    cannot be met when the cap is smaller than the required set.
     """
     data = np.asarray(melt_pool_data, dtype=np.float64)
     if data.ndim != 2 or data.shape[1] != 2 or data.shape[0] < 2:
         raise ValueError("melt_pool_data must have shape (n, 2) with n >= 2.")
     if not np.isfinite(data).all():
         raise ValueError("melt_pool_data must contain only finite values.")
-    if (n_modes is None) == (tolerance is None):
-        raise ValueError("Provide exactly one of n_modes or tolerance.")
+    if n_modes is None and tolerance is None:
+        raise ValueError("Provide either n_modes, tolerance, or both.")
+    if n_modes is not None and (
+        not isinstance(n_modes, (int, np.integer)) or n_modes < 1
+    ):
+        raise ValueError("n_modes must be a positive integer.")
 
     time_values = data[:, 0]
     signal = data[:, 1]
@@ -101,6 +108,10 @@ def compute_spectral_components(
     fft_values = np.fft.rfft(signal)
     frequencies = np.fft.rfftfreq(n_samples, d=dt)
     candidate_bins = np.arange(1, fft_values.size)
+    if n_modes is not None and n_modes > fft_values.size:
+        raise ValueError(
+            f"n_modes cannot exceed {fft_values.size} for this time series."
+        )
 
     # Parseval energy represented by each positive-frequency cosine.  Interior
     # rFFT bins represent a conjugate pair; the Nyquist bin does not.
@@ -128,17 +139,21 @@ def compute_spectral_components(
             + 1
         )
         selected_bins = energy_order[:retained_count]
-    else:
-        if not isinstance(n_modes, (int, np.integer)) or n_modes < 1:
-            raise ValueError("n_modes must be a positive integer.")
-        if n_modes > fft_values.size:
-            raise ValueError(
-                f"n_modes cannot exceed {fft_values.size} for this time series."
+        if n_modes is not None and selected_bins.size > n_modes - 1:
+            warnings.warn(
+                f"Requested tolerance requires {selected_bins.size + 1} modes; "
+                f"limiting the result to {n_modes} modes, so the tolerance "
+                "will not be met.",
+                RuntimeWarning,
+                stacklevel=2,
             )
+            selected_bins = selected_bins[: n_modes - 1]
+    else:
         selected_bins = candidate_bins[: n_modes - 1]
 
-    # Frequency order is convenient for evaluation and deterministic output.
+    # Return modes in frequency order after any energy-ranked selection and cap.
     selected_bins = np.sort(selected_bins)
+
     amplitudes = energy_weights[selected_bins] * np.abs(fft_values[selected_bins])
     amplitudes /= n_samples
     phases = np.angle(fft_values[selected_bins])
@@ -172,7 +187,7 @@ def create_melt_pool(
             spectral_array = compute_spectral_components(
                 data,
                 n_modes=n_modes,
-                tolerance=component_tolerance if n_modes is None else None,
+                tolerance=component_tolerance,
             )
             spectral_array[:, 0] *= scale
 
diff --git a/tests/test_api.py b/tests/test_api.py
index 4f8aed0..8d29432 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -379,6 +379,39 @@ def test_tolerance_selects_minimum_modes_and_meets_rmse(self):
         assert np.sqrt(np.mean((values - reconstructed) ** 2)) <= 0.03
         assert compute_required_modes(data, 0.03) == 2
 
+    def test_mode_cap_retains_highest_energy_tolerance_modes(self):
+        sampling_frequency = 1000.0
+        time = np.arange(1000) / sampling_frequency
+        values = (
+            1.0
+            + 0.1 * np.cos(2.0 * np.pi * 20.0 * time)
+            + 0.9 * np.cos(2.0 * np.pi * 170.0 * time)
+        )
+        data = np.column_stack([time, values])
+
+        with pytest.warns(RuntimeWarning, match="tolerance will not be met"):
+            spectral_array = compute_spectral_components(
+                data, n_modes=2, tolerance=0.01
+            )
+
+        assert spectral_array.shape == (2, 3)
+        assert spectral_array[1, 1] == pytest.approx(170.0)
+
+    def test_tolerance_modes_are_returned_in_frequency_order(self):
+        sampling_frequency = 1000.0
+        time = np.arange(1000) / sampling_frequency
+        values = (
+            1.0
+            + 0.1 * np.cos(2.0 * np.pi * 20.0 * time)
+            + 0.9 * np.cos(2.0 * np.pi * 170.0 * time)
+        )
+
+        spectral_array = compute_spectral_components(
+            np.column_stack([time, values]), tolerance=0.01
+        )
+
+        assert spectral_array[:, 1].tolist() == pytest.approx([0.0, 20.0, 170.0])
+
     def test_tolerance_zero_reconstructs_even_length_signal(self):
         time = 0.25 + np.arange(100) / 100.0
         values = 3.0 + 0.2 * np.cos(2.0 * np.pi * 5.0 * time)
@@ -398,9 +431,26 @@ def test_compute_spectral_components_invalid_input(self):
             compute_spectral_components(np.array([[0.0, 1.0]]), 1)
         with pytest.raises(ValueError, match="shape"):
             compute_spectral_components(np.ones((4, 1)), 2)
-        with pytest.raises(ValueError, match="exactly one"):
+        with pytest.raises(ValueError, match="either n_modes"):
             compute_spectral_components(np.ones((4, 2)))
 
+    @pytest.mark.parametrize("n_modes", [0, -1, 1.5])
+    def test_compute_spectral_components_rejects_invalid_mode_counts(
+        self, sample_time_series_data, n_modes
+    ):
+        with pytest.raises(ValueError, match="positive integer"):
+            compute_spectral_components(sample_time_series_data, n_modes=n_modes)
+
+    def test_tolerance_rejects_mode_count_above_available_bins(
+        self, sample_time_series_data
+    ):
+        with pytest.raises(ValueError, match="cannot exceed"):
+            compute_spectral_components(
+                sample_time_series_data,
+                n_modes=sample_time_series_data.shape[0],
+                tolerance=0.0,
+            )
+
 
 # =============================================================================
 # Tests for create_melt_pool