diff --git a/src/metrics/dilaton-axion-ad.jl b/src/metrics/dilaton-axion-ad.jl
index 6bacbbbb..c770effe 100644
--- a/src/metrics/dilaton-axion-ad.jl
+++ b/src/metrics/dilaton-axion-ad.jl
@@ -22,12 +22,12 @@ A(a, θ, δ, W, Δhat) = δ^2 - Δhat * (W * a * sin(θ))^2
     R = M
 
     # check these for the normalisation term R
-    βb = β / b
-    βa = β / a
-    βab = β / (a * b)
+    βb = β == zero(β) ? zero(β) : β / b
+    βa = β == zero(β) ? zero(β) : β / a
+    βab = β == zero(β) ? zero(β) : β / (a * b)
 
     Σ₀ = Σ(r, a, θ)
-    Δ₀ = Δ(r, R, a)
+    Δ₀ = Δ(r, 2R, a)
     Δhat₀ = Δhat(Δ₀, β, b, r, βb, R)
     Σhat₀ = Σhat(Σ₀, β, b, r, βb, a, θ, R)
     δ₀ = δ(r, b, a)
@@ -68,7 +68,9 @@ end
 
 metric_components(m::DilatonAxion{T}, rθ) where {T} =
     __DilatonAxionAD.metric_components(m.M, m.a, m.β, m.b, rθ)
-inner_radius(m::DilatonAxion{T}) where {T} =
-    m.M + m.b + √((m.M + m.b)^2 - m.a^2 + m.β^2 - (m.M - 2m.b) * m.M * (m.β / m.b)^2)
+function inner_radius(m::DilatonAxion{T}) where {T}
+    βb = m.β == zero(m.β) ? zero(m.β) : m.β / m.b
+    m.M + m.b + √((m.M + m.b)^2 - m.a^2 + m.β^2 - (m.M - 2m.b) * m.M * βb^2)
+end
 
 export DilatonAxion
diff --git a/test/smoke-tests/special-radii.jl b/test/smoke-tests/special-radii.jl
index 3d89ce83..e08cdfaf 100644
--- a/test/smoke-tests/special-radii.jl
+++ b/test/smoke-tests/special-radii.jl
@@ -13,6 +13,8 @@ using StaticArrays
         JohannsenMetric(M = 1.0, a = 0.998, α13 = 1.0),
         JohannsenMetric(M = 1.0, a = 0.998, α22 = 1.0),
         DilatonAxion(M = 1.0, a = 0.6, β = -0.5, b = 0.1),
+        KerrMetric(M = 1.0, a = 0.0),
+        DilatonAxion(M = 1.0, a = 0.0, b = 0.0, β = 0.0),
     )
 
     @testset "iscos" begin
@@ -26,7 +28,9 @@ using StaticArrays
                 8.99437445480357,
                 2.8482863127671534,
                 1.1306596884484472,
-                32.95283734688169,
+                29.701502242023523,
+                6.00000000,
+                6.00000000,
             ],
         )
             isco_r = Gradus.isco(m)