diff --git a/test/rulesets/Base/array.jl b/test/rulesets/Base/array.jl
index 233a85125..d6e379e50 100644
--- a/test/rulesets/Base/array.jl
+++ b/test/rulesets/Base/array.jl
@@ -1,4 +1,4 @@
-@testset "constructors" begin
+@testset "Array constructors" begin
 
     # We can't use test_rrule here (as it's currently implemented) because the elements of
     # the array have arbitrary values. The only thing we can do is ensure that we're getting
diff --git a/test/rulesets/Base/arraymath.jl b/test/rulesets/Base/arraymath.jl
index 4b30eafab..9f4df7428 100644
--- a/test/rulesets/Base/arraymath.jl
+++ b/test/rulesets/Base/arraymath.jl
@@ -1,4 +1,4 @@
-@testset "arraymath" begin
+@testset "arraymath.jl" begin
     @testset "inv(::Matrix{$T})" for T in (Float64, ComplexF64)
         B = generate_well_conditioned_matrix(T, 3)
         test_frule(inv, B)
diff --git a/test/rulesets/Base/base.jl b/test/rulesets/Base/base.jl
index e6dadaf47..820c1a3de 100644
--- a/test/rulesets/Base/base.jl
+++ b/test/rulesets/Base/base.jl
@@ -1,4 +1,4 @@
-@testset "base" begin
+@testset "base.jl" begin
     @testset "copysign" begin
         # don't go too close to zero as the numerics may jump over it yielding wrong results
         @testset "at $y" for y in (-1.1, 0.1, 100.0)  
diff --git a/test/rulesets/LinearAlgebra/dense.jl b/test/rulesets/LinearAlgebra/dense.jl
index da6fbf0d4..c7413dbb3 100644
--- a/test/rulesets/LinearAlgebra/dense.jl
+++ b/test/rulesets/LinearAlgebra/dense.jl
@@ -1,4 +1,4 @@
-@testset "dense" begin
+@testset "dense LinearAlgebra" begin
     @testset "dot" begin
         @testset "Vector{$T}" for T in (Float64, ComplexF64)
             test_frule(dot, randn(T, 3), randn(T, 3))
diff --git a/test/rulesets/Random/random.jl b/test/rulesets/Random/random.jl
index cf2a41595..4f1ccd3a8 100644
--- a/test/rulesets/Random/random.jl
+++ b/test/rulesets/Random/random.jl
@@ -5,7 +5,7 @@ struct NormalDistribution
 end
 Random.rand(d::NormalDistribution) = d.μ + d.σ*randn()
 
-@testset "random" begin
+@testset "Random" begin
     rng_types = [MersenneTwister]
     isdefined(Random, :Xoshiro) && push!(rng_types, getfield(Random, :Xoshiro))
     
diff --git a/test/runtests.jl b/test/runtests.jl
index cd6a15334..61548644b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -22,55 +22,58 @@ union!(JuliaInterpreter.compiled_modules, Any[Base, Base.Broadcast, Compat, Line
 
 Random.seed!(1) # Set seed that all testsets should reset to.
 
-function include_test(path::String)
-    println("Testing $path:")  # print so TravisCI doesn't timeout due to no output
-    @time Base.include(@__MODULE__(), path) do ex
-        Meta.isexpr(ex, :macrocall) && ex.args[1] == Symbol("@testset") || return ex
-        return :(@interpret (() -> $ex)())  # interpret testsets using JuliaInterpreter
+function include_test(path)
+    if isempty(ARGS) || any(occursin(a, path) for a in ARGS)
+        println("Testing $path:")  # print so TravisCI doesn't timeout due to no output
+        @time Base.include(@__MODULE__(), path) do ex
+            Meta.isexpr(ex, :macrocall) && ex.args[1] == Symbol("@testset") || return ex
+            return :(@interpret (() -> $ex)())  # interpret testsets using JuliaInterpreter
+        end
+    else
+        # If you provide ARGS like so, then it runs only matching testsets: 
+        # Pkg.test("ChainRules", test_args = ["index", "LinearAlgebra"])
+        println("(Not testing $path)")
     end
 end
 
-println("Testing ChainRules.jl")
-@testset "ChainRules" begin
-    include_test("test_helpers.jl")
+if isempty(ARGS)
+    println("Testing ChainRules.jl")
+else
+    println("Testing ChainRules.jl with test_args = ", ARGS)
+end
+
+@testset "ChainRules" begin  # One overall @testset ensures it keeps going after failures
+    include("test_helpers.jl")
     println()
-    @testset "rulesets" begin
-        @testset "Core" begin
-            include_test("rulesets/Core/core.jl")
-        end
 
-        @testset "Base" begin
-            include_test("rulesets/Base/base.jl")
-            include_test("rulesets/Base/fastmath_able.jl")
-            include_test("rulesets/Base/evalpoly.jl")
-            include_test("rulesets/Base/array.jl")
-            include_test("rulesets/Base/arraymath.jl")
-            include_test("rulesets/Base/indexing.jl")
-            include_test("rulesets/Base/mapreduce.jl")
-            include_test("rulesets/Base/sort.jl")
-        end
-        println()
+    # Each file puts all tests inside one or more @testset blocks
+    include_test("rulesets/Base/base.jl")
+    include_test("rulesets/Base/fastmath_able.jl")
+    include_test("rulesets/Base/evalpoly.jl")
+    include_test("rulesets/Base/array.jl")
+    include_test("rulesets/Base/arraymath.jl")
+    include_test("rulesets/Base/indexing.jl")
+    include_test("rulesets/Base/mapreduce.jl")
+    include_test("rulesets/Base/sort.jl")
 
-        @testset "Statistics" begin
-            include_test("rulesets/Statistics/statistics.jl")
-        end
-        println()
+    println()
 
-        @testset "LinearAlgebra" begin
-            include_test("rulesets/LinearAlgebra/dense.jl")
-            include_test("rulesets/LinearAlgebra/norm.jl")
-            include_test("rulesets/LinearAlgebra/matfun.jl")
-            include_test("rulesets/LinearAlgebra/structured.jl")
-            include_test("rulesets/LinearAlgebra/symmetric.jl")
-            include_test("rulesets/LinearAlgebra/factorization.jl")
-            include_test("rulesets/LinearAlgebra/blas.jl")
-            include_test("rulesets/LinearAlgebra/lapack.jl")
-        end
-        println()
+    include_test("rulesets/Statistics/statistics.jl")
 
-        @testset "Random" begin
-            include_test("rulesets/Random/random.jl")
-        end
-        println()
-    end
+    println()
+
+    include_test("rulesets/LinearAlgebra/dense.jl")
+    include_test("rulesets/LinearAlgebra/norm.jl")
+    include_test("rulesets/LinearAlgebra/matfun.jl")
+    include_test("rulesets/LinearAlgebra/structured.jl")
+    include_test("rulesets/LinearAlgebra/symmetric.jl")
+    include_test("rulesets/LinearAlgebra/factorization.jl")
+    include_test("rulesets/LinearAlgebra/blas.jl")
+    include_test("rulesets/LinearAlgebra/lapack.jl")
+
+    println()
+
+    include_test("rulesets/Random/random.jl")
+
+    println()
 end