diff --git a/R-package/tests/testthat/test_GPModel_non_Gaussian_data.R b/R-package/tests/testthat/test_GPModel_non_Gaussian_data.R
index 3f911522..fad7a1fe 100644
--- a/R-package/tests/testthat/test_GPModel_non_Gaussian_data.R
+++ b/R-package/tests/testthat/test_GPModel_non_Gaussian_data.R
@@ -1038,10 +1038,12 @@ if(Sys.getenv("GPBOOST_ALL_TESTS") == "GPBOOST_ALL_TESTS"){
       if(inv_method == "iterative") {
         tolerance_loc_1 <- TOLERANCE_ITERATIVE
         tolerance_loc_2 <- TOLERANCE_ITERATIVE
+        tolerance_loc_3 <- 2*TOLERANCE_ITERATIVE
         loop_cg_PC = c("pivoted_cholesky", "vadu", "fitc")
       } else {
         tolerance_loc_1 <- TOLERANCE_STRICT
         tolerance_loc_2 <- TOLERANCE_MEDIUM
+        tolerance_loc_3 <-TOLERANCE_STRICT
         loop_cg_PC = c("vadu")
       }
       nsim_var_pred <- 10000
@@ -1111,7 +1113,7 @@ if(Sys.getenv("GPBOOST_ALL_TESTS") == "GPBOOST_ALL_TESTS"){
                                           predict_cov_mat = TRUE, predict_response = FALSE, 
                                           cov_pars = cov_pars_pred_eval, X_pred = X_test), file='NUL')
           expect_lt(sum(abs(pred$mu-expected_mu)),tolerance_loc_1)
-          expect_lt(sum(abs(as.vector(pred$cov)-expected_cov)),tolerance_loc_1)
+          expect_lt(sum(abs(as.vector(pred$cov)-expected_cov)),tolerance_loc_3)
           capture.output( pred <- predict(gp_model, y=y, gp_coords_pred = coord_test, 
                                           predict_var = TRUE, predict_response = FALSE, 
                                           cov_pars = cov_pars_pred_eval, X_pred = X_test), file='NUL')
diff --git a/R-package/tests/testthat/test_z_GPBoost_algorithm.R b/R-package/tests/testthat/test_z_GPBoost_algorithm.R
index b87c0d93..5df181e6 100644
--- a/R-package/tests/testthat/test_z_GPBoost_algorithm.R
+++ b/R-package/tests/testthat/test_z_GPBoost_algorithm.R
@@ -264,7 +264,9 @@ if(Sys.getenv("NO_GPBOOST_ALGO_TESTS") != "NO_GPBOOST_ALGO_TESTS"){
       expect_lt(abs(opt_params$best_score-1.224379), TOLERANCE)
       
       # Parameter tuning with 'tune.pars.bayesian.optimization'
-      source("https://raw.githubusercontent.com/fabsig/GPBoost/master/helpers/R_package_tune_pars_bayesian_optimization.R")# Load required function
+      suppressWarnings({
+        source("https://raw.githubusercontent.com/fabsig/GPBoost/master/helpers/R_package_tune_pars_bayesian_optimization.R")# Load required function
+      })
       other_params <- list(objective = "regression_l2", max_depth = 6, num_leaves = 2^10)
       search_space = list("learning_rate" = c(0.1,1))
       crit = makeMBOInfillCritCB() # other criterion options: makeMBOInfillCritEI()