diff --git a/docs/user-guide/amor/amor-reduction.ipynb b/docs/user-guide/amor/amor-reduction.ipynb
index 01ffaca2..04115d19 100644
--- a/docs/user-guide/amor/amor-reduction.ipynb
+++ b/docs/user-guide/amor/amor-reduction.ipynb
@@ -172,7 +172,7 @@
     "from ess.reflectometry.tools import scale_reflectivity_curves_to_overlap\n",
     "results_scaled = dict(zip(\n",
     "    results.keys(),\n",
-    "    scale_reflectivity_curves_to_overlap(results.values()),\n",
+    "    scale_reflectivity_curves_to_overlap(results.values())[0],\n",
     "    strict=True\n",
     "))\n",
     "sc.plot(results_scaled, norm='log', vmin=1e-5)"
diff --git a/src/ess/reflectometry/tools.py b/src/ess/reflectometry/tools.py
index 341fa4f0..86823efc 100644
--- a/src/ess/reflectometry/tools.py
+++ b/src/ess/reflectometry/tools.py
@@ -170,28 +170,43 @@ def _interpolate_on_qgrid(curves, grid):
 
 def scale_reflectivity_curves_to_overlap(
     curves: Sequence[sc.DataArray],
-    return_scaling_factors=False,
-) -> list[sc.DataArray] | list[sc.scalar]:
+    critical_edge_interval: tuple[sc.Variable, sc.Variable] | None = None,
+) -> tuple[list[sc.DataArray], list[sc.Variable]]:
     '''Make the curves overlap by scaling all except the first by a factor.
     The scaling factors are determined by a maximum likelihood estimate
     (assuming the errors are normal distributed).
 
+    If :code:`critical_edge_interval` is provided then all curves are scaled.
+
     All curves must be have the same unit for data and the Q-coordinate.
 
     Parameters
     ---------
     curves:
         the reflectivity curves that should be scaled together
-    return_scaling_factor:
-        If True the return value of the function
-        is a list of the scaling factors that should be applied.
-        If False (default) the function returns the scaled curves.
+    critical_edge_interval:
+        a tuple denoting an interval that is known to belong
+        to the critical edge, i.e. where the reflectivity is
+        known to be 1.
 
     Returns
     ---------
     :
-        A list of scaled reflectivity curves or a list of scaling factors.
+        A list of scaled reflectivity curves and a list of the scaling factors.
     '''
+    if critical_edge_interval is not None:
+        q = next(iter(curves)).coords['Q']
+        N = (
+            ((q >= critical_edge_interval[0]) & (q < critical_edge_interval[1]))
+            .sum()
+            .value
+        )
+        edge = sc.DataArray(
+            data=sc.ones(dims=('Q',), shape=(N,), with_variances=True),
+            coords={'Q': sc.linspace('Q', *critical_edge_interval, N + 1)},
+        )
+        curves, factors = scale_reflectivity_curves_to_overlap([edge, *curves])
+        return curves[1:], factors[1:]
     if len({c.data.unit for c in curves}) != 1:
         raise ValueError('The reflectivity curves must have the same unit')
     if len({c.coords['Q'].unit for c in curves}) != 1:
@@ -214,13 +229,11 @@ def cost(scaling_factors):
         return np.nansum((r_scaled - r_avg) ** 2 * inv_v_scaled)
 
     sol = opt.minimize(cost, [1.0] * (len(curves) - 1))
-    scaling_factors = (1.0, *sol.x)
-    if return_scaling_factors:
-        return [sc.scalar(x) for x in scaling_factors]
+    scaling_factors = (1.0, *map(float, sol.x))
     return [
         scaling_factor * curve
         for scaling_factor, curve in zip(scaling_factors, curves, strict=True)
-    ]
+    ], scaling_factors
 
 
 def combine_curves(
diff --git a/tests/tools_test.py b/tests/tools_test.py
index b447fcf4..193e9245 100644
--- a/tests/tools_test.py
+++ b/tests/tools_test.py
@@ -1,6 +1,7 @@
 # SPDX-License-Identifier: BSD-3-Clause
 # Copyright (c) 2023 Scipp contributors (https://github.com/scipp)
 import scipp as sc
+from numpy.testing import assert_allclose as np_assert_allclose
 from scipp.testing import assert_allclose
 
 from ess.reflectometry.tools import combine_curves, scale_reflectivity_curves_to_overlap
@@ -20,16 +21,17 @@ def test_reflectivity_curve_scaling():
     )
     data.variances[:] = 0.1
 
-    curves = scale_reflectivity_curves_to_overlap(
+    curves, factors = scale_reflectivity_curves_to_overlap(
         (curve(data, 0, 0.3), curve(0.8 * data, 0.2, 0.7), curve(0.1 * data, 0.6, 1.0)),
     )
 
     assert_allclose(curves[0].data, data, rtol=sc.scalar(1e-5))
     assert_allclose(curves[1].data, 0.5 * data, rtol=sc.scalar(1e-5))
     assert_allclose(curves[2].data, 0.25 * data, rtol=sc.scalar(1e-5))
+    np_assert_allclose((1, 0.5 / 0.8, 0.25 / 0.1), factors, 1e-4)
 
 
-def test_reflectivity_curve_scaling_return_factors():
+def test_reflectivity_curve_scaling_with_critical_edge():
     data = sc.concat(
         (
             sc.ones(dims=['Q'], shape=[10], with_variances=True),
@@ -39,14 +41,19 @@ def test_reflectivity_curve_scaling_return_factors():
     )
     data.variances[:] = 0.1
 
-    factors = scale_reflectivity_curves_to_overlap(
-        (curve(data, 0, 0.3), curve(0.8 * data, 0.2, 0.7), curve(0.1 * data, 0.6, 1.0)),
-        return_scaling_factors=True,
+    curves, factors = scale_reflectivity_curves_to_overlap(
+        (
+            2 * curve(data, 0, 0.3),
+            curve(0.8 * data, 0.2, 0.7),
+            curve(0.1 * data, 0.6, 1.0),
+        ),
+        critical_edge_interval=(sc.scalar(0.01), sc.scalar(0.05)),
     )
 
-    assert_allclose(factors[0], sc.scalar(1.0), rtol=sc.scalar(1e-5))
-    assert_allclose(factors[1], sc.scalar(0.5 / 0.8), rtol=sc.scalar(1e-5))
-    assert_allclose(factors[2], sc.scalar(0.25 / 0.1), rtol=sc.scalar(1e-5))
+    assert_allclose(curves[0].data, data, rtol=sc.scalar(1e-5))
+    assert_allclose(curves[1].data, 0.5 * data, rtol=sc.scalar(1e-5))
+    assert_allclose(curves[2].data, 0.25 * data, rtol=sc.scalar(1e-5))
+    np_assert_allclose((0.5, 0.5 / 0.8, 0.25 / 0.1), factors, 1e-4)
 
 
 def test_combined_curves():