diff --git a/CHANGELOG.md b/CHANGELOG.md
index f0ea6b7..e683f2c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,11 +10,16 @@ adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 ### Added
   - `Base.literal_pow` definitions for `KVector{1}` that produce `KVector` results.
 
+### Changed
+  - Natural exponential are only optimized for `KVector` types whose `BitIndices` uniformly square
+    to the same value.
+
 ### Fixed
   - `OddCliffordNumber` constructors now fail to operate on scalars unless there is exactly one odd
     element in the algebra.
   - Broken bullets in `AbstractCliffordNumber` docstring.
   - `StackOverflowError` in `KVector{0}` exponentiation.
+  - Incorrect natural exponentials in algebras with non-uniform sign signatures.
 
 ## [0.1.6] - 2024-06-27
 
diff --git a/src/math/exponential.jl b/src/math/exponential.jl
index 500a060..0890bfd 100644
--- a/src/math/exponential.jl
+++ b/src/math/exponential.jl
@@ -145,11 +145,11 @@ See also: [`exppi`](@ref), [`exptau`](@ref).
 function exp(x::AbstractCliffordNumber)
     T = exponential_type(x)
     Tx = convert(T, x)
-    sq = mul(Tx, Tx)
-    if isscalar(sq)
-        mag = abs(x)
-        scalar(sq) < 0 && return T(cos(mag))  + Tx * (sin(mag) / mag)
-        scalar(sq) > 0 && return T(cosh(mag)) + Tx * (sinh(mag) / mag)
+    # Check that all basis blades of the type square to the same sign, too
+    if allequal(sign_of_square(b) for b in BitIndices(x)) && isscalar(x^2)
+        mag = abs(x)    # should be faster to calculate directly from input type (it may be shorter)
+        scalar(x^2) < 0 && return T(cos(mag))  + Tx * (sin(mag) / mag)
+        scalar(x^2) > 0 && return T(cosh(mag)) + Tx * (sinh(mag) / mag)
         return one(T) + Tx
     end
     return exp_taylor(x)