diff --git a/hls4ml/model/optimizer/passes/infer_precision.py b/hls4ml/model/optimizer/passes/infer_precision.py
index d17971cca9..2a8982e549 100644
--- a/hls4ml/model/optimizer/passes/infer_precision.py
+++ b/hls4ml/model/optimizer/passes/infer_precision.py
@@ -2,6 +2,7 @@
 from collections.abc import Iterable
 
 import numpy as np
+from fxpmath import Fxp
 
 from hls4ml.model.optimizer import ConfigurableOptimizerPass
 from hls4ml.model.types import (
@@ -573,9 +574,17 @@ def _infer_par_act_precision(self, node, types_to_infer):
         # For threshold relu, set the parameter precision to be the input precision by default;
         # for other parametrized activations, just allow the default precision to be used.
         # Can override these values in the configuration by explicitly setting them.
-        if 'param_t' in types_to_infer and node.get_attr('activation').lower() == 'thresholdedrelu':
-            in_type = node.get_input_variable().type.precision
-            node.attributes['param_t'].precision = in_type
+        if 'param_t' in types_to_infer:
+            if node.get_attr('activation').lower() == 'thresholdedrelu':
+                # For threshold relu, set the parameter precision to be the input precision by default;
+                in_type = node.get_input_variable().type.precision
+                node.attributes['param_t'].precision = in_type
+                inferred_types.append('param_t')
+            else:
+                # find a constant to represent the values
+                param = node.get_attr('activ_param')
+                precision = _get_precision_from_constant(param)
+                node.attributes['param_t'].precision = precision
             inferred_types.append('param_t')
 
         return inferred_types
@@ -594,3 +603,33 @@ def _infer_prelu_act_precision(self, node, types_to_infer):
             inferred_types.append('param_t')
 
         return inferred_types
+
+
+def _get_precision_from_constant(value: int | float, max_width=8):
+    """A utility function to find a fixed type to store the constant
+
+    Arguments:
+        value (int or float): the constant value
+        max_width (int, optional): the maximum fixed width (+ 1 if signed). Defaults to 8
+
+    Returns:
+        FixedPrecisionType: the type to use
+    """
+    if value == 0:
+        return FixedPrecisionType(width=1, integer=1, signed=False)
+
+    signed = value < 0
+    absval = abs(value)
+    # check if power of 2
+    mantissa, exp = np.frexp(absval)
+    if mantissa == 0.5:  # is it a power of 2?
+        # One could consider returning an ExponentPrecisionType here.
+        # Decided on FixedPrecisionType everywhere since ExponentPrecisionType is less supported
+        return FixedPrecisionType(1 + signed, exp, signed)
+
+    # now is the general case. First try Fxp
+    fxpval = Fxp(value, signed=signed)
+    if isinstance(fxpval.n_word, int) and fxpval.n_word <= max_width:
+        return FixedPrecisionType(fxpval.n_word, signed + fxpval.n_int, signed)
+
+    return FixedPrecisionType(signed + max_width, signed + exp, signed)
diff --git a/hls4ml/model/types.py b/hls4ml/model/types.py
index a83dbbf14e..f794604f4f 100644
--- a/hls4ml/model/types.py
+++ b/hls4ml/model/types.py
@@ -270,7 +270,7 @@ def min(self):
 
     @property
     def max(self):
-        return 2.0 ** (self.integer - 1) - 2.0**-self.fractional
+        return 2.0 ** (self.integer - self.signed) - 2.0**-self.fractional
 
 
 class XnorPrecisionType(PrecisionType):
diff --git a/pyproject.toml b/pyproject.toml
index 6f25ffee75..d8b35e743a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -25,7 +25,7 @@ classifiers = [
   "Topic :: Software Development :: Libraries :: Python Modules",
 ]
 dynamic = [ "version" ]
-dependencies = [ "h5py", "numpy", "pydigitalwavetools==1.1", "pyyaml", "quantizers" ]
+dependencies = [ "fxpmath", "h5py", "numpy", "pydigitalwavetools==1.1", "pyyaml", "quantizers" ]
 
 optional-dependencies.da = [ "da4ml>=0.2.1,<=0.4" ]
 optional-dependencies.doc = [
diff --git a/test/pytest/test_auto_precision.py b/test/pytest/test_auto_precision.py
index a57a913b20..041a3e3c53 100644
--- a/test/pytest/test_auto_precision.py
+++ b/test/pytest/test_auto_precision.py
@@ -17,6 +17,7 @@
 from tensorflow.keras.models import Sequential
 
 import hls4ml
+from hls4ml.model.optimizer.passes.infer_precision import _get_precision_from_constant
 
 test_root_path = Path(__file__).parent
 
@@ -254,3 +255,31 @@ def test_auto_precision_dense(keras_model_dense, data_1d, io_type, backend):
     y_keras = model.predict(data).flatten()
     y_hls = hls_model.predict(data).flatten()
     np.testing.assert_allclose(y_keras, y_hls, rtol=2e-2, atol=5e-2, verbose=True)
+
+
+@pytest.mark.parametrize(
+    "val, expected_width",
+    [
+        (0, 1),
+        (-1024, 2),
+        (1024, 1),
+        (0.03125, 1),
+        (-0.03125, 2),
+        (1.25, 3),
+        (-1.25, 4),
+        (1.1, 8),
+        (-1.1, 9),
+    ],
+)
+def test_precision_from_constant_unit(val, expected_width):
+    """Test determining precision needed for a constant."""
+    max_width = 8
+    fp = _get_precision_from_constant(val, max_width)
+
+    assert fp.min <= val <= fp.max
+    assert fp.width == expected_width
+    assert fp.signed == (val < 0)
+
+    quantum = 2.0**-fp.fractional
+    if expected_width < max_width:
+        assert val % quantum == 0