diff --git a/test/main.h b/test/main.h
index 59a777312..52c27117b 100644
--- a/test/main.h
+++ b/test/main.h
@@ -892,6 +892,14 @@ std::string type_name() {
   return type_name(T());
 }
 
+template <typename DataContainer>
+void setRandomDataInRange(DataContainer& data_container, typename DataContainer::Scalar min_value,
+                          typename DataContainer::Scalar max_value) {
+  for (Eigen::Index i = 0; i < data_container.size(); ++i) {
+    data_container.data()[i] = Eigen::internal::random<typename DataContainer::Scalar>(min_value, max_value);
+  }
+}
+
 using namespace Eigen;
 
 /**
diff --git a/unsupported/test/cxx11_tensor_assign.cpp b/unsupported/test/cxx11_tensor_assign.cpp
index 47b6361d9..29d73c4cb 100644
--- a/unsupported/test/cxx11_tensor_assign.cpp
+++ b/unsupported/test/cxx11_tensor_assign.cpp
@@ -250,8 +250,13 @@ static void test_auto_resize() {
 static void test_compound_assign() {
   Tensor<int, 1> start_tensor(10);
   Tensor<int, 1> offset_tensor(10);
-  start_tensor.setRandom();
-  offset_tensor.setRandom();
+  setRandomDataInRange(start_tensor, -1000, 1000);
+  setRandomDataInRange(offset_tensor, -1000, 1000);
+
+  // Avoid division by zero in the final compound assignment check.
+  for (int i = 0; i < 10; ++i) {
+    if (offset_tensor(i) == 0) offset_tensor(i) = 1;
+  }
 
   Tensor<int, 1> tensor = start_tensor;
   tensor += offset_tensor;
diff --git a/unsupported/test/cxx11_tensor_block_eval.cpp b/unsupported/test/cxx11_tensor_block_eval.cpp
index 0567b3c61..9281224a8 100644
--- a/unsupported/test/cxx11_tensor_block_eval.cpp
+++ b/unsupported/test/cxx11_tensor_block_eval.cpp
@@ -13,6 +13,16 @@
 using Eigen::internal::TensorBlockDescriptor;
 using Eigen::internal::TensorExecutor;
 
+template <typename T, int NumDims, int Layout>
+static void setRandomForBinaryProduct(Tensor<T, NumDims, Layout>& tensor) {
+  EIGEN_IF_CONSTEXPR((std::is_integral<T>::value && !std::is_same<T, bool>::value)) {
+    setRandomDataInRange(tensor, T(-1000), T(1000));
+  }
+  else {
+    tensor.setRandom();
+  }
+}
+
 // -------------------------------------------------------------------------- //
 // Utility functions to generate random tensors, blocks, and evaluate them.
 
@@ -220,8 +230,8 @@ template <typename T, int NumDims, int Layout>
 static void test_eval_tensor_binary_expr_block() {
   DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
   Tensor<T, NumDims, Layout> lhs(dims), rhs(dims);
-  lhs.setRandom();
-  rhs.setRandom();
+  setRandomForBinaryProduct(lhs);
+  setRandomForBinaryProduct(rhs);
 
   VerifyBlockEvaluator<T, NumDims, Layout>(lhs * rhs, [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
 }
diff --git a/unsupported/test/cxx11_tensor_intdiv.cpp b/unsupported/test/cxx11_tensor_intdiv.cpp
index 3d818e077..358f98492 100644
--- a/unsupported/test/cxx11_tensor_intdiv.cpp
+++ b/unsupported/test/cxx11_tensor_intdiv.cpp
@@ -81,11 +81,15 @@ void test_unsigned_64bit() {
 }
 
 void test_powers_32bit() {
+  const int32_t int32_max = (std::numeric_limits<int32_t>::max)();
   for (int expon = 1; expon < 31; expon++) {
     int32_t div = (1 << expon);
     for (int num_expon = 0; num_expon < 32; num_expon++) {
-      int32_t start_num = (1 << num_expon) - 100;
-      int32_t end_num = (1 << num_expon) + 100;
+      const int64_t pivot = int64_t(1) << num_expon;
+      int32_t start_num = pivot > int32_max ? int32_max : static_cast<int32_t>(pivot);
+      int32_t end_num = start_num;
+      start_num = (std::max)(int32_t(0), start_num - 100);
+      end_num = static_cast<int32_t>((std::min)(int64_t(int32_max), int64_t(end_num) + 100));
       if (start_num < 0) start_num = 0;
       for (int32_t num = start_num; num < end_num; num++) {
         Eigen::internal::TensorIntDivisor<int32_t> divider = Eigen::internal::TensorIntDivisor<int32_t>(div);
diff --git a/unsupported/test/cxx11_tensor_reduction.cpp b/unsupported/test/cxx11_tensor_reduction.cpp
index 81dc0ce53..d28019991 100644
--- a/unsupported/test/cxx11_tensor_reduction.cpp
+++ b/unsupported/test/cxx11_tensor_reduction.cpp
@@ -335,7 +335,7 @@ static void test_tensor_maps() {
   TensorMap<Tensor<const int, 4, DataLayout>> tensor_map_const(inputs, 2, 3, 5, 7);
   const TensorMap<Tensor<const int, 4, DataLayout>> tensor_map_const_const(inputs, 2, 3, 5, 7);
 
-  tensor_map.setRandom();
+  setRandomDataInRange(tensor_map, -1000, 1000);
   array<ptrdiff_t, 2> reduction_axis;
   reduction_axis[0] = 1;
   reduction_axis[1] = 3;
diff --git a/unsupported/test/cxx11_tensor_ref.cpp b/unsupported/test/cxx11_tensor_ref.cpp
index 7696558c8..d8f99c16c 100644
--- a/unsupported/test/cxx11_tensor_ref.cpp
+++ b/unsupported/test/cxx11_tensor_ref.cpp
@@ -45,9 +45,9 @@ static void test_simple_lvalue_ref() {
 
 static void test_simple_rvalue_ref() {
   Tensor<int, 1> input1(6);
-  input1.setRandom();
+  setRandomDataInRange(input1, -1000, 1000);
   Tensor<int, 1> input2(6);
-  input2.setRandom();
+  setRandomDataInRange(input2, -1000, 1000);
 
   TensorRef<const Tensor<int, 1>> ref3(input1 + input2);
   TensorRef<const Tensor<int, 1>> ref4 = input1 + input2;
@@ -110,7 +110,7 @@ static void test_slice() {
 
 static void test_ref_of_trace() {
   Tensor<int, 2> input(6, 6);
-  input.setRandom();
+  setRandomDataInRange(input, -1000, 1000);
   int trace = 0;
   for (int i = 0; i < 6; ++i) {
     trace += input(i, i);
diff --git a/unsupported/test/cxx11_tensor_scan.cpp b/unsupported/test/cxx11_tensor_scan.cpp
index 30730f25e..8f0b3a243 100644
--- a/unsupported/test/cxx11_tensor_scan.cpp
+++ b/unsupported/test/cxx11_tensor_scan.cpp
@@ -85,7 +85,7 @@ template <int DataLayout>
 static void test_tensor_maps() {
   int inputs[20];
   TensorMap<Tensor<int, 1, DataLayout> > tensor_map(inputs, 20);
-  tensor_map.setRandom();
+  setRandomDataInRange(tensor_map, -1000, 1000);
 
   Tensor<int, 1, DataLayout> result = tensor_map.cumsum(0);