diff --git a/tedana/selection/_utils.py b/tedana/selection/_utils.py
index 3722bd991..a86a47070 100644
--- a/tedana/selection/_utils.py
+++ b/tedana/selection/_utils.py
@@ -41,6 +41,17 @@ def getelbow_cons(arr, return_val=False):
     """
     if arr.ndim != 1:
         raise ValueError('Parameter arr should be 1d, not {0}d'.format(arr.ndim))
+
+    if not arr.size:
+        raise ValueError(
+            "Empty array detected during elbow calculation. "
+            "This error happens when getelbow_cons is incorrectly called on no components. "
+            "If you see this message, please open an issue at "
+            "https://github.com/ME-ICA/tedana/issues with the full traceback and any data "
+            "necessary to reproduce this error, so that we create additional data checks to "
+            "prevent this from happening."
+        )
+
     arr = np.sort(arr)[::-1]
     nk = len(arr)
     temp1 = [(arr[nk - 5 - ii - 1] > arr[nk - 5 - ii:nk].mean() + 2 * arr[nk - 5 - ii:nk].std())
@@ -79,6 +90,17 @@ def getelbow(arr, return_val=False):
     """
     if arr.ndim != 1:
         raise ValueError('Parameter arr should be 1d, not {0}d'.format(arr.ndim))
+
+    if not arr.size:
+        raise ValueError(
+            "Empty array detected during elbow calculation. "
+            "This error happens when getelbow is incorrectly called on no components. "
+            "If you see this message, please open an issue at "
+            "https://github.com/ME-ICA/tedana/issues with the full traceback and any data "
+            "necessary to reproduce this error, so that we create additional data checks to "
+            "prevent this from happening."
+        )
+
     arr = np.sort(arr)[::-1]
     n_components = arr.shape[0]
     coords = np.array([np.arange(n_components), arr])
diff --git a/tedana/selection/tedica.py b/tedana/selection/tedica.py
index 2032309e3..02c0d021c 100644
--- a/tedana/selection/tedica.py
+++ b/tedana/selection/tedica.py
@@ -245,13 +245,23 @@ def kundu_selection_v2(comptable, n_echos, n_vols):
     # Compute elbows from other elbows
     f05, _, f01 = getfbounds(n_echos)
     kappas_nonsig = comptable.loc[comptable['kappa'] < f01, 'kappa']
+    if not kappas_nonsig.size:
+        LGR.warning(
+            "No nonsignificant kappa values detected. "
+            "Only using elbow calculated from all kappa values."
+        )
+        kappas_nonsig_elbow = np.nan
+    else:
+        kappas_nonsig_elbow = getelbow(kappas_nonsig, return_val=True)
+
+    kappas_all_elbow = getelbow(comptable['kappa'], return_val=True)
+
     # NOTE: Would an elbow from all Kappa values *ever* be lower than one from
-    # a subset of lower values?
-    kappa_elbow = np.min((getelbow(kappas_nonsig, return_val=True),
-                          getelbow(comptable['kappa'], return_val=True)))
-    rho_elbow = np.mean((getelbow(comptable.loc[ncls, 'rho'], return_val=True),
-                         getelbow(comptable['rho'], return_val=True),
-                         f05))
+    # a subset of lower (i.e., nonsignificant) values?
+    kappa_elbow = np.nanmin((kappas_all_elbow, kappas_nonsig_elbow))
+    rhos_ncls_elbow = getelbow(comptable.loc[ncls, 'rho'], return_val=True)
+    rhos_all_elbow = getelbow(comptable['rho'], return_val=True)
+    rho_elbow = np.mean((rhos_ncls_elbow, rhos_all_elbow, f05))
 
     # Provisionally accept components based on Kappa and Rho elbows
     acc_prov = ncls[(comptable.loc[ncls, 'kappa'] >= kappa_elbow) &
diff --git a/tedana/tests/test_selection_utils.py b/tedana/tests/test_selection_utils.py
new file mode 100644
index 000000000..7288f8c6e
--- /dev/null
+++ b/tedana/tests/test_selection_utils.py
@@ -0,0 +1,45 @@
+"""Tests for the tedana.selection._utils module."""
+import numpy as np
+import pytest
+
+from tedana.selection import _utils
+
+
+def test_getelbow_smoke():
+    """A smoke test for the getelbow function."""
+    arr = np.random.random(100)
+    idx = _utils.getelbow(arr)
+    assert isinstance(idx, np.integer)
+
+    val = _utils.getelbow(arr, return_val=True)
+    assert isinstance(val, float)
+
+    # Running an empty array should raise a ValueError
+    arr = np.array([])
+    with pytest.raises(ValueError):
+        _utils.getelbow(arr)
+
+    # Running a 2D array should raise a ValueError
+    arr = np.random.random((100, 100))
+    with pytest.raises(ValueError):
+        _utils.getelbow(arr)
+
+
+def test_getelbow_cons():
+    """A smoke test for the getelbow_cons function."""
+    arr = np.random.random(100)
+    idx = _utils.getelbow_cons(arr)
+    assert isinstance(idx, np.integer)
+
+    val = _utils.getelbow_cons(arr, return_val=True)
+    assert isinstance(val, float)
+
+    # Running an empty array should raise a ValueError
+    arr = np.array([])
+    with pytest.raises(ValueError):
+        _utils.getelbow_cons(arr)
+
+    # Running a 2D array should raise a ValueError
+    arr = np.random.random((100, 100))
+    with pytest.raises(ValueError):
+        _utils.getelbow_cons(arr)