diff --git a/CHANGES.rst b/CHANGES.rst
index a7633462e0..ac9ea231e8 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -49,6 +49,9 @@ extract_1d
 - Added a hook to bypass the ``extract_1d`` step for NIRISS SOSS data in
   the FULL subarray with warning. [#8225]
 
+- Fixed a bug in the ATOCA matrix solve for NIRISS SOSS that would cause failures on
+  good input data in some cases. [#8273]
+  
 - Added a trap in the NIRISS SOSS ATOCA algorithm for cases where nearly all
   pixels in the 2nd-order spectrum are flagged and would cause the step
   to fail. [#8265]
diff --git a/jwst/extract_1d/soss_extract/atoca.py b/jwst/extract_1d/soss_extract/atoca.py
index 1b8578a269..b53c668b25 100644
--- a/jwst/extract_1d/soss_extract/atoca.py
+++ b/jwst/extract_1d/soss_extract/atoca.py
@@ -12,8 +12,9 @@
 
 # General imports.
 import numpy as np
+import warnings
 from scipy.sparse import issparse, csr_matrix, diags
-from scipy.sparse.linalg import spsolve
+from scipy.sparse.linalg import spsolve, lsqr, MatrixRankWarning
 from scipy.interpolate import interp1d
 
 # Local imports.
@@ -1290,7 +1291,15 @@ def _solve(matrix, result):
         # Only solve for valid indices, i.e. wavelengths that are
         # covered by the pixels on the detector.
         # It will be a singular matrix otherwise.
-        sln[idx] = spsolve(matrix[idx, :][:, idx], result[idx])
+        warnings.filterwarnings(action='error', category=MatrixRankWarning)
+        try:
+            sln[idx] = spsolve(matrix[idx, :][:, idx], result[idx])
+        except MatrixRankWarning:
+            # on rare occasions spsolve's approximation of the matrix is not appropriate
+            # and fails on good input data. revert to different solver
+            log.info('ATOCA matrix solve failed with spsolve. Retrying with least-squares.')
+            sln[idx] = lsqr(matrix[idx, :][:, idx], result[idx])[0]
+        warnings.resetwarnings()
 
         return sln
 
diff --git a/jwst/regtest/test_niriss_soss.py b/jwst/regtest/test_niriss_soss.py
index b900b0318f..efb2253194 100644
--- a/jwst/regtest/test_niriss_soss.py
+++ b/jwst/regtest/test_niriss_soss.py
@@ -126,7 +126,24 @@ def test_niriss_soss_extras(rtdata_module, run_atoca_extras, fitsdiff_default_kw
     assert diff.identical, diff.report()
 
 
-@pytest.mark.bigdata
+@pytest.fixture(scope='module')
+def run_extract1d_spsolve_failure(jail, rtdata_module):
+    """
+    Test coverage for fix to error thrown when spsolve fails to find
+    a good solution in ATOCA and needs to be replaced with a least-
+    squares solver. Note this failure is architecture-dependent
+    and also only trips for specific values of the transform parameters.
+    Pin tikfac for faster runtime.
+    """
+    rtdata = rtdata_module
+    rtdata.get_data("niriss/soss/jw04098007001_04101_00001-seg003_nis_int01.fits")
+    args = ["extract_1d", rtdata.input,
+            "--soss_tikfac=3.1881637371089252e-15",
+            "--soss_transform=-0.00038201755227297866, -0.24237455427848956, 0.5404013401742825",
+            ]
+    Step.from_cmdline(args)
+
+
 @pytest.fixture(scope='module')
 def run_extract1d_null_order2(jail, rtdata_module):
     """
@@ -144,8 +161,23 @@ def run_extract1d_null_order2(jail, rtdata_module):
     Step.from_cmdline(args)
 
 
+@pytest.mark.bigdata
+def test_extract1d_spsolve_failure(rtdata_module, run_extract1d_spsolve_failure, fitsdiff_default_kwargs):
+
+    rtdata = rtdata_module
+
+    output = "jw04098007001_04101_00001-seg003_nis_int01_extract1dstep.fits"
+    rtdata.output = output
+
+    rtdata.get_truth(f"truth/test_niriss_soss_stages/{output}")
+
+    diff = FITSDiff(rtdata.output, rtdata.truth, **fitsdiff_default_kwargs)
+    assert diff.identical, diff.report()
+
+
 @pytest.mark.bigdata
 def test_extract1d_null_order2(rtdata_module, run_extract1d_null_order2, fitsdiff_default_kwargs):
+
     rtdata = rtdata_module
 
     output = "jw01201008001_04101_00001-seg003_nis_int72_extract1dstep.fits"