diff --git a/test/ica.jl b/test/ica.jl
index 2e9127d..543eecf 100644
--- a/test/ica.jl
+++ b/test/ica.jl
@@ -93,7 +93,7 @@ import StatsBase
         W = M.W
         @test W'C * W ≈ Matrix(I, k, k)
 
-        @test_throws StatsBase.ConvergenceException fit(ICA, X, k; do_whiten=true, tol=0.01)
+        @test_throws StatsBase.ConvergenceException fit(ICA, X, k; do_whiten=true, tol=1e-8, maxiter=2)
 
         # Use data of different type
 
diff --git a/test/ppca.jl b/test/ppca.jl
index 006831a..da617b7 100644
--- a/test/ppca.jl
+++ b/test/ppca.jl
@@ -103,7 +103,7 @@ import StatsBase
     @test outdim(M) == 4
     @test mean(M) == mval
     @test P'P ≈ Matrix(I, 4, 4)
-    @test all(isapprox.(reconstruct(M, transform(M, X)), reconstruct(M0, transform(M0, X)), atol=1e-3))
+    @test all(isapprox.(reconstruct(M, transform(M, X)), reconstruct(M0, transform(M0, X)), atol=1e-2))
 
     M = fit(PPCA, X; method=:em, mean=mval)
     @test loadings(M) ≈ W