diff --git a/pyrasa/utils/irasa_utils.py b/pyrasa/utils/irasa_utils.py
index f19b2c2..85d4571 100644
--- a/pyrasa/utils/irasa_utils.py
+++ b/pyrasa/utils/irasa_utils.py
@@ -49,14 +49,14 @@ def _get_windows(
 ) -> tuple[np.ndarray, np.ndarray]:
     """Generate a window function used for tapering"""
     low_bias_ratio = 0.9
-    max_time_bandwidth = 2.0
+    min_time_bandwidth = 2.0
     win_func_kwargs = copy(win_func_kwargs)
 
     # special settings in case multitapering is required
     if win_func == dsp.windows.dpss:
         time_bandwidth = dpss_settings['time_bandwidth']
-        if time_bandwidth < max_time_bandwidth:
-            raise ValueError(f'time_bandwidth should be >= {max_time_bandwidth} for good tapers')
+        if time_bandwidth > min_time_bandwidth:
+            raise ValueError(f'time_bandwidth should be >= {min_time_bandwidth} for good tapers')
 
         n_taps = int(np.floor(time_bandwidth - 1))
         win_func_kwargs.update(
diff --git a/tests/test_irasa_sprint.py b/tests/test_irasa_sprint.py
index bc752f3..8d1a954 100644
--- a/tests/test_irasa_sprint.py
+++ b/tests/test_irasa_sprint.py
@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 from neurodsp.utils.sim import set_random_seed
 
 from pyrasa.irasa import irasa_sprint
@@ -80,7 +81,7 @@ def test_irasa_sprint_settings(ts4sprint):
     # test dpss
     import scipy.signal as dsp
 
-    sgramm_ap, sgramm_p, freqs_ir, times_ir = irasa_sprint(
+    irasa_sprint(
         ts4sprint[np.newaxis, :],
         fs=500,
         band=(1, 100),
@@ -89,3 +90,16 @@ def test_irasa_sprint_settings(ts4sprint):
         # smooth=False,
         # n_avgs=[3, 7, 11],
     )
+
+    # test too much bandwidht
+    with pytest.raises(ValueError):
+        irasa_sprint(
+            ts4sprint[np.newaxis, :],
+            fs=500,
+            band=(1, 100),
+            win_func=dsp.windows.dpss,
+            dpss_settings_time_bandwidth=1,
+            freq_res=0.5,
+            # smooth=False,
+            # n_avgs=[3, 7, 11],
+        )
diff --git a/tests/test_peak_detect.py b/tests/test_peak_detect.py
index f1652a9..c8ac781 100644
--- a/tests/test_peak_detect.py
+++ b/tests/test_peak_detect.py
@@ -24,6 +24,18 @@ def test_peak_detection(oscillation, fs, osc_freq):
     assert bool(np.isclose(pe_filt['cf'][0], osc_freq, atol=2))
 
 
+@pytest.mark.parametrize('fs, exponent', [(500, -1)], scope='session')
+def test_no_peak_detection(fixed_aperiodic_signal, fs):
+    f_range = [1, 250]
+    # test whether recombining periodic and aperiodic spectrum is equivalent to the original spectrum
+    freqs, psd = dsp.welch(fixed_aperiodic_signal, fs, nperseg=int(4 * fs))
+    freq_logical = np.logical_and(freqs >= f_range[0], freqs <= f_range[1])
+    freqs, psd = freqs[freq_logical], psd[freq_logical]
+    # test whether we can reconstruct the peaks correctly
+    pe_params = get_peak_params(psd[np.newaxis, :], freqs, min_peak_height=0.1)
+    assert pe_params.shape[0] == 0
+
+
 @pytest.mark.parametrize('osc_freq, fs', [(10, 500)], scope='session')
 def test_peak_detection_setings(oscillation, fs, osc_freq):
     f_range = [1, 250]