diff --git a/pyewjn/dielectric/nam_dielectric_coefficient_approximator.py b/pyewjn/dielectric/nam_dielectric_coefficient_approximator.py
index f39a4d4..c906bdd 100644
--- a/pyewjn/dielectric/nam_dielectric_coefficient_approximator.py
+++ b/pyewjn/dielectric/nam_dielectric_coefficient_approximator.py
@@ -4,7 +4,12 @@ import pyewjn.dielectric.low_k_nam
 
 from pyewjn.baskets import CalculationParams, CalculationConstants
 
-from typing import Tuple
+from typing import Tuple, Callable
+import logging
+
+
+_logger = logging.getLogger(__name__)
+
 
 FIXED_LARGE_MOMENTUM = 1e8
 
@@ -141,10 +146,10 @@ def get_unapproximated_nam_dielectric(
 	u_c: float,
 	params: CalculationParams,
 	constants: CalculationConstants = CalculationConstants(),
-):
+) -> Callable[[float], float]:
 
 	sigma_n = params.omega_p**2 * params.tau / (4 * np.pi)
-	coeffs = get_nam_dielectric_coefficients(
+	dedim = get_dedimensionalised_parameters(
 		params.omega,
 		sigma_n,
 		params.tau,
@@ -153,4 +158,19 @@ def get_unapproximated_nam_dielectric(
 		params.t_c,
 		constants.c_light,
 	)
-	return coeffs.eps(u_c)
+	prefactor = 4j * np.pi * dedim.b
+
+	def eps_ret(u: float) -> float:
+		if u * dedim.a * 100 < abs(dedim.xi + 1j * dedim.nu):
+			_logger.info("Falling to low k version")
+			return prefactor * pyewjn.dielectric.low_k_nam.sigma_nam_alk(
+				dedim.xi, u * dedim.a, dedim.nu, dedim.t
+			)
+		elif u < u_c:
+			return prefactor * pyewjn.dielectric.sigma_nam.sigma_nam(
+				dedim.xi, u * dedim.a, dedim.nu, dedim.t
+			)
+		else:
+			return 1
+
+	return eps_ret
diff --git a/tests/dielectric/test_nam_dielectric_coefficient_approximator.py b/tests/dielectric/test_nam_dielectric_coefficient_approximator.py
index dbe7199..f0c241d 100644
--- a/tests/dielectric/test_nam_dielectric_coefficient_approximator.py
+++ b/tests/dielectric/test_nam_dielectric_coefficient_approximator.py
@@ -137,3 +137,31 @@ def test_nam_eps():
 	np.testing.assert_allclose(
 		eps_to_test(1e17), 1, rtol=1e-6, err_msg="above cutoff bad"
 	)
+
+
+def test_unapproximated_nam_eps():
+	u_c = 1e15
+	eps_to_test = pyewjn.dielectric.nam_dielectric_coefficient_approximator.get_unapproximated_nam_dielectric(
+		u_c,
+		CalculationParams(
+			omega=1e9, omega_p=3.54491e15, tau=1e-14, v_f=2e6, t_rel=0.8, t_c=1e11
+		),
+	)
+
+	np.testing.assert_allclose(
+		eps_to_test(10),
+		-3.789672906817707e10 + 3.257134605133221e8j,
+		rtol=1e-3,
+		err_msg="below u_l bad",
+	)
+
+	np.testing.assert_allclose(
+		eps_to_test(1e10),
+		-2.645743e8 + 2.293455422222e6j,
+		rtol=1e-3,
+		err_msg="linear region bad",
+	)
+
+	np.testing.assert_allclose(
+		eps_to_test(1e17), 1, rtol=1e-6, err_msg="above cutoff bad"
+	)