diff --git a/docs/src/manual/configuration.md b/docs/src/manual/configuration.md
index f73f7e07..08fd2a8d 100644
--- a/docs/src/manual/configuration.md
+++ b/docs/src/manual/configuration.md
@@ -7,7 +7,12 @@ CurrentModule = IntervalArithmetic
 The IntervalArithmetic.jl package provides a [`configure`](@ref) function (not exported) that allows users to fine-tune certain aspects of the package’s behavior. This is particularly useful for controlling trade-offs between computational speed and rigor.
 
 !!! warning
-    The [`configure`](@ref) function redefines methods that alter the internal behavior of IntervalArithmetic. This persists across the current Julia session and affect all subsequent interval arithmetic computations.
+    The [`configure`](@ref) function redefines methods that alter the internal behavior of IntervalArithmetic. This persists across the current Julia session and affects all subsequent interval arithmetic computations.
+
+    A new configuration takes effect in code that starts running after `configure` returns to the Julia prompt. Code that is already running keeps using the previous configuration (see the section on world age in the Julia manual).
+    In particular, calling `configure` from a function leaves the old behavior intact while the rest of the function runs. Use `Base.invokelatest` to call into the new configuration from the same function.
+
+    Each change invalidates every compiled method that depends on the modified option, so configuration changes may trigger recompilation delays before using the new configuration.
 
 Each keyword argument sets a specific configuration option:
 - `numtype`: control the default numerical type used to represent the bounds of the intervals.
diff --git a/src/intervals/construction.jl b/src/intervals/construction.jl
index e05b173a..2ae2e874 100644
--- a/src/intervals/construction.jl
+++ b/src/intervals/construction.jl
@@ -101,15 +101,18 @@ for irr ∈ (:(:π), :(:γ), :(:catalan)) # irrationals supported by MPFR
     @eval _round(::Type{T}, a::Irrational{$irr}, r::RoundingMode) where {T<:NumTypes} =
         __round(T, BigFloat(a, r), r)
 end
-# irrationals not supported by MPFR, use their exact formula ℯ = exp(1), φ = (1+sqrt(5))/2
-_round(::Type{T}, ::Irrational{:ℯ}, r::RoundingMode{:Down}) where {T<:NumTypes} =
-    __round(T, inf(exp(bareinterval(BigFloat, 1))), r)
-_round(::Type{T}, ::Irrational{:ℯ}, r::RoundingMode{:Up}) where {T<:NumTypes} =
-    __round(T, sup(exp(bareinterval(BigFloat, 1))), r)
-_round(::Type{T}, ::Irrational{:φ}, r::RoundingMode{:Down}) where {T<:NumTypes} =
-    __round(T, inf((bareinterval(BigFloat, 1) + sqrt(bareinterval(BigFloat, 5))) / bareinterval(BigFloat, 2)), r)
-_round(::Type{T}, ::Irrational{:φ}, r::RoundingMode{:Up}) where {T<:NumTypes} =
-    __round(T, sup((bareinterval(BigFloat, 1) + sqrt(bareinterval(BigFloat, 5))) / bareinterval(BigFloat, 2)), r)
+# irrationals not supported by MPFR, use their exact formula ℯ = exp(1), φ = (1+sqrt(5))/2.
+# The rounding mode is fixed to `:correct` rather than taken from `default_rounding()`:
+# the enclosure of a constant must be rigorous whatever the configuration, and the
+# generated `bareinterval(::Type{T}, ::AbstractIrrational)` bakes the result in at its
+# first generation, which method invalidation does not track.
+_round(::Type{T}, ::Irrational{:ℯ}, r::RoundingMode) where {T<:NumTypes} =
+    __round(T, _fround(exp, IntervalRounding{:correct}(), one(BigFloat), r), r)
+function _round(::Type{T}, ::Irrational{:φ}, r::RoundingMode) where {T<:NumTypes}
+    ir = IntervalRounding{:correct}()
+    sqrt5 = _fround(sqrt, ir, BigFloat(5), r)
+    return __round(T, _fround(/, ir, _fround(+, ir, one(BigFloat), sqrt5, r), BigFloat(2), r), r)
+end
 # floats
 __round(::Type{T}, a, r::RoundingMode) where {T<:AbstractFloat} = T(a, r)
 # rationals
diff --git a/test/IntervalArithmetic.jl b/test/IntervalArithmetic.jl
index 393469a9..52025f91 100644
--- a/test/IntervalArithmetic.jl
+++ b/test/IntervalArithmetic.jl
@@ -309,5 +309,17 @@ end
         @test nextfloat(inf(z128)) == sup(z128)
     end
 
+    # irrational enclosures are rigorous whatever the configured rounding mode
+    try
+        IntervalArithmetic.configure(rounding = :none)
+        for irr ∈ (MathConstants.ℯ, MathConstants.golden), T ∈ (Float64, BigFloat)
+            y = Base.invokelatest(bareinterval, T, irr)
+            @test in_interval(irr, y)
+            @test inf(y) < sup(y)
+        end
+    finally
+        IntervalArithmetic.configure(rounding = :correct)
+    end
+
     @test_throws ArgumentError("only irrationals from MathConstants or IrrationalConstants.jl are supported") bareinterval(Float64, Base.Irrational{:foo}())
 end