diff --git a/src/highlevel/coloring.jl b/src/highlevel/coloring.jl
index c11ddabb..3217533b 100644
--- a/src/highlevel/coloring.jl
+++ b/src/highlevel/coloring.jl
@@ -78,7 +78,7 @@ function (alg::ApproximateJacobianSparsity)(ad::AutoSparseFiniteDiff, f::F, x; f
     cache = FiniteDiff.JacobianCache(x, fx)
     J = fill!(similar(fx, length(fx), length(x)), 0)
     x_ = similar(x)
-    ε = eps(eltype(x)) * 100
+    ε = ifelse(alg.epsilon === nothing, eps(eltype(x)) * 100, alg.epsilon)
     for _ in 1:ntrials
         randn!(rng, x_)
         J_cache = FiniteDiff.finite_difference_jacobian(f, x, cache)
@@ -95,7 +95,7 @@ function (alg::ApproximateJacobianSparsity)(ad::AutoSparseFiniteDiff, f!::F, fx,
     J = fill!(similar(fx, length(fx), length(x)), 0)
     J_cache = similar(J)
     x_ = similar(x)
-    ε = eps(eltype(x)) * 100
+    ε = ifelse(alg.epsilon === nothing, eps(eltype(x)) * 100, alg.epsilon)
     for _ in 1:ntrials
         randn!(rng, x_)
         FiniteDiff.finite_difference_jacobian!(J_cache, f!, x_, cache)
diff --git a/src/highlevel/common.jl b/src/highlevel/common.jl
index 45c380e5..1f609fed 100644
--- a/src/highlevel/common.jl
+++ b/src/highlevel/common.jl
@@ -114,7 +114,7 @@ end
 
 """
     ApproximateJacobianSparsity(; ntrials = 5, rng = Random.default_rng(),
-        alg = GreedyD1Color())
+        epsilon = nothing, alg = GreedyD1Color())
 
 Use `ntrials` random vectors to compute the sparsity pattern of the Jacobian. This is an
 approximate method and the sparsity pattern may not be exact.
@@ -124,17 +124,21 @@ approximate method and the sparsity pattern may not be exact.
     - `ntrials`: The number of random vectors to use for computing the sparsity pattern
     - `rng`: The random number generator used for generating the random vectors
     - `alg`: The algorithm used for computing the matrix colors
+    - `epsilon`: For Finite Differencing based Jacobian Approximations, any number smaller
+      than `epsilon` is considered to be zero. If `nothing` is specified, then this value
+      is calculated as `100 * eps(eltype(x))`
 """
-struct ApproximateJacobianSparsity{R <: AbstractRNG,
-    A <: ArrayInterface.ColoringAlgorithm} <: AbstractSparsityDetection
+struct ApproximateJacobianSparsity{R <: AbstractRNG, A <: ArrayInterface.ColoringAlgorithm,
+    E} <: AbstractSparsityDetection
     ntrials::Int
     rng::R
     alg::A
+    epsilon::E
 end
 
-function ApproximateJacobianSparsity(; ntrials::Int = 3,
+function ApproximateJacobianSparsity(; ntrials::Int = 3, epsilon = nothing,
         rng::AbstractRNG = Random.default_rng(), alg = GreedyD1Color())
-    return ApproximateJacobianSparsity(ntrials, rng, alg)
+    return ApproximateJacobianSparsity(ntrials, rng, alg, epsilon)
 end
 
 # No one should be using this currently