diff --git a/src/curve_fit.jl b/src/curve_fit.jl
index e45fd26..24801bc 100755
--- a/src/curve_fit.jl
+++ b/src/curve_fit.jl
@@ -16,13 +16,26 @@ StatsAPI.residuals(lfr::LsqFitResult) = lfr.resid
 mse(lfr::LsqFitResult) = rss(lfr) / dof(lfr)
 isconverged(lsr::LsqFitResult) = lsr.converged
 
-function check_data_health(xdata, ydata)
-    if any(ismissing, xdata) || any(ismissing, ydata)
-        error("Data contains `missing` values and a fit cannot be performed")
+function check_data_health(xdata, ydata, wt = [])
+    if any(ismissing, xdata)
+        error("The independent variable (`x`) contains `missing` values and a fit cannot be performed")
     end
-    if any(isinf, xdata) || any(isinf, ydata) || any(isnan, xdata) || any(isnan, ydata)
-        error("Data contains `Inf` or `NaN` values and a fit cannot be performed")
+    if any(ismissing, ydata)
+        error("The dependent variable (`y`) contains `missing` values and a fit cannot be performed")
     end
+    if any(ismissing, wt)
+        error("Weight data contains `missing` values and a fit cannot be performed")
+    end
+    if any(!isfinite, xdata)
+        error("The independent variable (`x`) contains non-finite (e.g. `Inf`, `NaN`) values and a fit cannot be performed")
+    end
+    if any(!isfinite, ydata)
+        error("The dependent variable (`y`) contains non-finite (e.g. `Inf`, `NaN`) values and a fit cannot be performed")
+    end
+    if any(!isfinite, wt)
+        error("Weight contains non-finite (e.g. `Inf`, `NaN`) values and a fit cannot be performed")
+    end
+        
 end
 
 # provide a method for those who have their own Jacobian function
@@ -174,7 +187,7 @@ function curve_fit(
     inplace=false,
     kwargs...,
 )
-    check_data_health(xdata, ydata)
+    check_data_health(xdata, ydata, wt)
     # construct a weighted cost function, with a vector weight for each ydata
     # for example, this might be wt = 1/sigma where sigma is some error term
     u = sqrt.(wt) # to be consistant with the matrix form
@@ -198,7 +211,7 @@ function curve_fit(
     inplace=false,
     kwargs...,
 )
-    check_data_health(xdata, ydata)
+    check_data_health(xdata, ydata, wt)
     u = sqrt.(wt) # to be consistant with the matrix form
 
     if inplace
@@ -220,7 +233,7 @@ function curve_fit(
     p0::AbstractArray;
     kwargs...,
 )
-    check_data_health(xdata, ydata)
+    check_data_health(xdata, ydata, wt)
 
     # as before, construct a weighted cost function with where this
     # method uses a matrix weight.
@@ -244,7 +257,7 @@ function curve_fit(
     p0::AbstractArray;
     kwargs...,
 )
-    check_data_health(xdata, ydata)
+    check_data_health(xdata, ydata, wt)
 
     u = cholesky(wt).U
 
diff --git a/test/curve_fit.jl b/test/curve_fit.jl
index 0be8e3e..50694ab 100755
--- a/test/curve_fit.jl
+++ b/test/curve_fit.jl
@@ -2,17 +2,15 @@ using LsqFit, Test, StableRNGs, LinearAlgebra
 @testset "curve fit" begin
     # before testing the model, check whether missing/null data is rejected
     tdata = [rand(1:10, 5)..., missing]
-    @test_throws ErrorException(
-        "Data contains `missing` values and a fit cannot be performed",
-    ) LsqFit.check_data_health(tdata, tdata)
+    @test_throws ErrorException("The independent variable (`x`) contains `missing` values and a fit cannot be performed") LsqFit.check_data_health(tdata, tdata)
     tdata = [rand(1:10, 5)..., Inf]
-    @test_throws ErrorException(
-        "Data contains `Inf` or `NaN` values and a fit cannot be performed",
-    ) LsqFit.check_data_health(tdata, tdata)
+    @test_throws ErrorException("The independent variable (`x`) contains non-finite (e.g. `Inf`, `NaN`) values and a fit cannot be performed") LsqFit.check_data_health(tdata, tdata)
     tdata = [rand(1:10, 5)..., NaN]
-    @test_throws ErrorException(
-        "Data contains `Inf` or `NaN` values and a fit cannot be performed",
-    ) LsqFit.check_data_health(tdata, tdata)
+    @test_throws ErrorException("The independent variable (`x`) contains non-finite (e.g. `Inf`, `NaN`) values and a fit cannot be performed") LsqFit.check_data_health(tdata, tdata)
+   
+    # fitting noisy data to an exponential model
+    # TODO: Change to `.-x` when 0.5 support is dropped
+    model(x, p) = p[1] .* exp.(-x .* p[2])
 
     for T in (Float64, BigFloat)
         # fitting noisy data to an exponential model
diff --git a/test/curve_fit_inplace.jl b/test/curve_fit_inplace.jl
index e20c3f0..9ea63b5 100644
--- a/test/curve_fit_inplace.jl
+++ b/test/curve_fit_inplace.jl
@@ -168,6 +168,26 @@ using LsqFit, Test, StableRNGs, LinearAlgebra
     )
     @test fit_wt.converged
 
+    @testset "bad input" begin
+        xxdata = copy(collect(xdata))
+        yydata = copy(ydata)
+        WWT = 1 ./ sqrt.(yvars)
+        x1 = xxdata[1]
+        y1 = yydata[1]
+        wt1 = WWT[1]
+        for x in (x1, Inf, -Inf, NaN), y in (y1, Inf, -Inf, NaN), wt in (wt1, Inf, -Inf, NaN)
+
+            xxdata[1] = x
+            yydata[1] = y
+            WWT[1] = wt
+            if x == x1 && y == y1 && wt == wt1
+                @test_nowarn curve_fit(model, jacobian_model, xxdata, yydata, WWT, [0.5, 0.5]; maxIter=100)
+            else
+                @test_throws ErrorException curve_fit(model, jacobian_model, xxdata, yydata, WWT, [0.5, 0.5]; maxIter=100)
+            end
+        end
+    end
+
     println("\t Inplace with weights")
     fit_inplace_wt = @time curve_fit(
         model_inplace,