diff --git a/Project.toml b/Project.toml
index dc435c4..51354aa 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "FiniteDifferences"
 uuid = "26cc04aa-876d-5657-8c51-4c34ba976000"
-version = "0.12.10"
+version = "0.12.11"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/rand_tangent.jl b/src/rand_tangent.jl
index 4ca2548..930a3c7 100644
--- a/src/rand_tangent.jl
+++ b/src/rand_tangent.jl
@@ -1,7 +1,9 @@
 """
     rand_tangent([rng::AbstractRNG,] x)
 
-Returns a randomly generated tangent vector appropriate for the primal value `x`.
+Returns a arbitary tangent vector _appropriate_ for the primal value `x`.
+Note that despite the name, no promises on the statistical randomness are made.
+Rather it is an arbitary value, that is generated using the `rng`.
 """
 rand_tangent(x) = rand_tangent(Random.GLOBAL_RNG, x)
 
@@ -11,11 +13,21 @@ rand_tangent(rng::AbstractRNG, x::AbstractString) = NoTangent()
 
 rand_tangent(rng::AbstractRNG, x::Integer) = NoTangent()
 
-rand_tangent(rng::AbstractRNG, x::T) where {T<:Number} = randn(rng, T)
+# Try and make nice numbers with short decimal representations for good error messages
+# while also not biasing the sample space too much
+function rand_tangent(rng::AbstractRNG, x::T) where {T<:Number}
+    # multiply by 9 to give a bigger range of values tested: no so tightly clustered around 0.
+    return round(9 * randn(rng, T), sigdigits=5, base=2)
+end
+rand_tangent(rng::AbstractRNG, x::Float64) = rand(rng, -9:0.01:9)
+function rand_tangent(rng::AbstractRNG, x::ComplexF64)
+    return ComplexF64(rand(rng, -9:0.1:9), rand(rng, -9:0.1:9))
+end
+
+#BigFloat/MPFR is finicky about short numbers, this doesn't always work as well as it should
 
-# TODO: right now Julia don't allow `randn(rng, BigFloat)`
-# see: https://github.com/JuliaLang/julia/issues/17629
-rand_tangent(rng::AbstractRNG, ::BigFloat) = big(randn(rng))
+# multiply by 9 to give a bigger range of values tested: no so tightly clustered around 0.
+rand_tangent(rng::AbstractRNG, ::BigFloat) = round(big(9 * randn(rng)), sigdigits=5, base=2)
 
 rand_tangent(rng::AbstractRNG, x::StridedArray) = rand_tangent.(Ref(rng), x)
 rand_tangent(rng::AbstractRNG, x::Adjoint) = adjoint(rand_tangent(rng, parent(x)))
diff --git a/test/rand_tangent.jl b/test/rand_tangent.jl
index 92a2d50..f5815e8 100644
--- a/test/rand_tangent.jl
+++ b/test/rand_tangent.jl
@@ -86,4 +86,14 @@ using FiniteDifferences: rand_tangent
         @test x + rand_tangent(x) isa typeof(x)
         @test x + (rand_tangent(x) + rand_tangent(x)) isa typeof(x)
     end
+
+    # Julia 1.6 changed to using Ryu printing algorithm and seems better at printing short
+    VERSION > v"1.6" && @testset "niceness of printing" begin
+        for i in 1:50
+            @test length(string(rand_tangent(1.0))) <= 6
+            @test length(string(rand_tangent(1.0 + 1.0im))) <= 12
+            @test length(string(rand_tangent(1f0))) <= 12
+            @test length(string(rand_tangent(big"1.0"))) <= 12
+        end
+    end
 end