diff --git a/CHANGES.rst b/CHANGES.rst
index 1c6391d6..5a8463b6 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -7,21 +7,33 @@ Unreleased 4.x
 Changes:
 
 - Includes the `main` branch in continuous integration automation.
+- [**BREAKING**] Previously when tallying the uncertainty for a `UFloat` object, the
+   contribution from other `UFloat` objects with `std_dev == 0` were excluded. Now this
+   special casing for `std_dev == 0` has been removed so that the contribution from all
+   contributing `UFloat` objects is included. This changes the behavior in certain
+   corner cases where `UFloat` `f` is derived from `UFloat` `x`, `x` has `x.s == 0`, but
+   the derivative of `f` with respect to `x` is `NaN`. For example, previously
+   `(-1)**ufloat(1, 0)` gave `-1.0+/-0`. The justification for this was that the second
+   `UFloat` with `std_dev` of `0` should be treated like a regular float. Now the same
+   calculation returns `-1.0+/-nan`. In this case the `UFloat` in the second argument
+   of the power operator is treated as a degenerate `UFloat`.
 
 Removes:
 
-- [*BREAKING*] Removes certain deprecated `umath` functions and
+- [**BREAKING**] Removes certain deprecated `umath` functions and
    `AffineScalarFunc`/`UFloat` methods. The following `umath` functions are removed:
    `ceil`, `copysign`, `fabs`, `factorial`, `floor`, `fmod`, `frexp`, `ldexp`, `modf`,
    `trunc`. The following `AffineScalarFunc`/`UFloat` methods are removed:
    `__floordiv__`, `__mod__`, `__abs__`, `__trunc__`, `__lt__`, `__le__`, `__gt__`,
    `__ge__`, `__bool__`.
-- [*BREAKING*] Previously it was possible for a `UFloat` object to compare equal to a
+- [**BREAKING**] Previously it was possible for a `UFloat` object to compare equal to a
    `float` object if the `UFloat` `standard_deviation` was zero and the `UFloat`
    `nominal_value` was equal to the `float`. Now, when an equality comparison is made
    between a `UFloat` object and another object, if the object is not a `UFloat` then
    the equality comparison is deferred to this other object. For the specific case of
    `float` this means that the equality comparison always returns `False`.
+- [**BREAKING**] The `uncertainties` package is generally dropping formal support for
+   edge cases involving `UFloat` objects with `std_dev == 0`.
 
 Unreleased
 ----------
diff --git a/doc/tech_guide.rst b/doc/tech_guide.rst
index 5a028cac..0ff7a653 100644
--- a/doc/tech_guide.rst
+++ b/doc/tech_guide.rst
@@ -197,16 +197,6 @@ This indicates that **the derivative required by linear error
 propagation theory is not defined** (a Monte-Carlo calculation of the
 resulting random variable is more adapted to this specific case).
 
-However, even in this case where the derivative at the nominal value
-is infinite, the :mod:`uncertainties` package **correctly handles
-perfectly precise numbers**:
-
->>> umath.sqrt(ufloat(0, 0))
-0.0+/-0
-
-is thus the correct result, despite the fact that the derivative of
-the square root is not defined in zero.
-
 .. _math_def_num_uncert:
 
 Mathematical definition of numbers with uncertainties
diff --git a/tests/test_power.py b/tests/test_power.py
index 6bfb44f6..90790f55 100644
--- a/tests/test_power.py
+++ b/tests/test_power.py
@@ -88,17 +88,10 @@ def test_power_derivatives(first_ufloat, second_ufloat, first_der, second_der):
 
 power_zero_std_dev_result_cases = [
     (0, p, 0),
-    (zero, p, 0),
-    (float("nan"), zero, 1),
-    (one, float("nan"), 1),
     (p, 0, 1),
     (zero, 0, 1),
     (-p, 0, 1),
-    (-10.3, zero, 1),
-    (0, zero, 1),
     (0.3, zero, 1),
-    (-p, zero, 1),
-    (zero, zero, 1),
     (p, zero, 1),
     (one, -3, 1),
     (one, -3.1, 1),
diff --git a/uncertainties/core.py b/uncertainties/core.py
index 85db46f9..9436057d 100644
--- a/uncertainties/core.py
+++ b/uncertainties/core.py
@@ -469,26 +469,10 @@ def error_components(self):
         object take scalar values (and are not a tuple, like what
         math.frexp() returns, for instance).
         """
-
-        # Calculation of the variance:
-        error_components = {}
-
-        for variable, derivative in self.derivatives.items():
-            # print "TYPE", type(variable), type(derivative)
-
-            # Individual standard error due to variable:
-
-            # 0 is returned even for a NaN derivative (in this case no
-            # multiplication by the derivative is performed): an exact
-            # variable obviously leads to no uncertainty in the
-            # functions that depend on it.
-            if variable._std_dev == 0:
-                # !!! Shouldn't the errors always be floats, as a
-                # convention of this module?
-                error_components[variable] = 0
-            else:
-                error_components[variable] = abs(derivative * variable._std_dev)
-
+        error_components = {
+            variable: abs(derivative * variable._std_dev)
+            for variable, derivative in self.derivatives.items()
+        }
         return error_components
 
     @property