diff --git a/src/univariate/continuous/exponential.jl b/src/univariate/continuous/exponential.jl
index 36ccd90..c239a35 100644
--- a/src/univariate/continuous/exponential.jl
+++ b/src/univariate/continuous/exponential.jl
@@ -6,21 +6,46 @@ function fit(::Type{Exponential}, m::AbstractMoments)
     return Exponential(mean(m))
 end
 
-function fit(::Type{Exponential}, lower::QuantilePoint, upper::QuantilePoint)
+function fit(::Type{Exponential}, lower::QuantilePoint, upper::Missing)
+    θ_lower = -lower.q/log(1-lower.p)
+    Exponential(θ_lower)
+end
+
+function fit(::Type{Exponential}, lower::Missing, upper::QuantilePoint)
+    θ_upper = -upper.q/log(1-upper.p)
+    Exponential(θ_upper)
+end
+
+function fit(dt::Type{Exponential}, lower::QuantilePoint, upper::QuantilePoint)
     # return average for the two quantiles
+    ismissing(lower.q) && return(fit(dt, missing, upper))
+    ismissing(upper.q) && return(fit(dt, lower, missing))
     θ_lower = -lower.q/log(1-lower.p)
     θ_upper = -upper.q/log(1-upper.p)
+    θ_lower ≈ θ_upper || @warn("Averaging scale for lower and upper quantile " * 
+        "for fitting expoenential distribution.")
     θ = (θ_lower + θ_upper)/2
     Exponential(θ)
 end
 
-function fit_mean_quantile(::Type{Exponential}, mean::Real, qp::QuantilePoint)
+function fit_mean_quantile(dt::Type{Exponential}, mean::Real, qp::QuantilePoint)
     # only fit to mean
+    warning("ignoring upper quantile when fitting Exponential to mean.")
+    fit_mean_quantile(dt, mean, missing)
+end
+
+function fit_mean_quantile(::Type{Exponential}, mean::Real, qp::Missing)
     fit(Type{Exponential}, AbstractMoments(mean))
 end
 
-function fit_mode_quantile(::Type{Exponential}, mode::Real, qp::QuantilePoint)
+function fit_mode_quantile(dt::Type{Exponential}, mode::Real, qp::QuantilePoint)
     # ignore mode (its always at 0)
+    mode != zero(mode) && @warn("ignoring mode when fitting Exponential.")
+    fit_mode_quantile(dt, missing, qp)
+end
+
+
+function fit_mode_quantile(::Type{Exponential}, mode::Missing, qp::QuantilePoint)
     θ = -qp.q/log(1-qp.p)
     Exponential(θ)
 end
diff --git a/test/exponential.jl b/test/exponential.jl
index ca4db47..31823c7 100644
--- a/test/exponential.jl
+++ b/test/exponential.jl
@@ -30,12 +30,17 @@ end;
 @testset "fit two quantiles" begin
     qpl = @qp_m(3)
     qpu = @qp_u(5)
-    d = fit(Exponential, qpl, qpu);
+    d = @test_logs (:warn,) fit(Exponential, qpl, qpu);
     #plot(d); 
     #plot!(fit_mode_quantile(Exponential, NaN, qpl))
     #plot!(fit_mode_quantile(Exponential, NaN, qpu))
     #vline!([3,5])
     @test quantile(d, qpl.p) < qpl.q
     @test quantile(d, qpu.p) > qpu.q
+    #
+    d = fit(Exponential, missing, qpu);
+    @test quantile.(d, [qpu.p]) ≈ [qpu.q]
+    d = fit(Exponential, qpl, missing);
+    @test quantile.(d, [qpl.p]) ≈ [qpl.q]
 end;