diff --git a/Project.toml b/Project.toml
index 8ea1659..c6f34e3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,10 +4,8 @@ authors = ["Andrew R. Winters <andrew.ross.winters@liu.se>", "Michael Schlottke-
 version = "0.1.0-pre"
 
 [deps]
-Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb"
 
 [compat]
-Reexport = "1"
 Trixi = "0.5.17"
 julia = "1.8"
diff --git a/src/TrixiShallowWater.jl b/src/TrixiShallowWater.jl
index f477853..b72b67e 100644
--- a/src/TrixiShallowWater.jl
+++ b/src/TrixiShallowWater.jl
@@ -1,13 +1,10 @@
 module TrixiShallowWater
 
-# import @reexport now to make it available for further imports/exports
-using Reexport: @reexport
-
-# Make all of Trixi.jl available to a user of this package
-@reexport using Trixi
+using Trixi: Trixi
 
 # Write your package code here.
 foo() = true
 bar() = false
+baz() = Trixi.examples_dir()
 
 end
diff --git a/test/Project.toml b/test/Project.toml
index 0c36332..034c50c 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,2 +1,6 @@
 [deps]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb"
+
+[compat]
+Trixi = "0.5"
diff --git a/test/runtests.jl b/test/runtests.jl
index 18a579c..909d0e2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,7 +1,24 @@
 using TrixiShallowWater
 using Test
 
-@testset "TrixiShallowWater.jl" begin
-  @test TrixiShallowWater.foo() == true
-  @test TrixiShallowWater.bar() == false
+# We run tests in parallel with CI jobs setting the `TRIXI_TEST` environment
+# variable to determine the subset of tests to execute.
+# By default, we just run the threaded tests since they are relatively cheap
+# and test a good amount of different functionality.
+const TRIXI_TEST = get(ENV, "TRIXI_TEST", "all")
+const TRIXI_MPI_NPROCS = clamp(Sys.CPU_THREADS, 2, 3)
+const TRIXI_NTHREADS = clamp(Sys.CPU_THREADS, 2, 3)
+
+@time @testset "TrixiShallowWater.jl tests" begin
+    @time if TRIXI_TEST == "all"
+        @test TrixiShallowWater.foo() == true
+        @test TrixiShallowWater.bar() == false
+        @test TrixiShallowWater.baz() isa String
+    end
+
+    @time if TRIXI_TEST == "all" || TRIXI_TEST == "upstream"
+        @testset "baz()" begin
+            @test TrixiShallowWater.baz() isa String
+        end
+    end
 end