diff --git a/test/adjoint.cpp b/test/adjoint.cpp
index 881d63951..8ecbcab4a 100644
--- a/test/adjoint.cpp
+++ b/test/adjoint.cpp
@@ -70,17 +70,6 @@ struct adjoint_specific<false> {
   }
 };
 
-template <typename MatrixType, typename Scalar = typename MatrixType::Scalar>
-MatrixType RandomMatrix(Index rows, Index cols, Scalar min, Scalar max) {
-  MatrixType M = MatrixType(rows, cols);
-  for (Index i = 0; i < rows; ++i) {
-    for (Index j = 0; j < cols; ++j) {
-      M(i, j) = Eigen::internal::random<Scalar>(min, max);
-    }
-  }
-  return M;
-}
-
 template <typename MatrixType>
 void adjoint(const MatrixType& m) {
   /* this test covers the following files:
diff --git a/test/cholesky.cpp b/test/cholesky.cpp
index a703b93ff..5c8ec85bb 100644
--- a/test/cholesky.cpp
+++ b/test/cholesky.cpp
@@ -505,7 +505,6 @@ template <typename Scalar>
 void cholesky_rowmajor_boundary() {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMatrixType;
-  typedef Matrix<Scalar, Dynamic, 1> VectorType;
 
   const Index sizes[] = {7, 8, 9, 15, 16, 17, 31, 32, 33};
   for (Index si = 0; si < Index(sizeof(sizes) / sizeof(sizes[0])); ++si) {
diff --git a/test/integer_types.cpp b/test/integer_types.cpp
index 142854cf2..bfda96e60 100644
--- a/test/integer_types.cpp
+++ b/test/integer_types.cpp
@@ -17,6 +17,7 @@
 template <typename MatrixType>
 void signed_integer_type_tests(const MatrixType& m) {
   typedef typename MatrixType::Scalar Scalar;
+  constexpr Scalar kMax = (Scalar(1) << ((8 * sizeof(Scalar) - 2) / 2)) - 1;
 
   enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };
   VERIFY(is_signed == 1);
@@ -24,26 +25,12 @@ void signed_integer_type_tests(const MatrixType& m) {
   Index rows = m.rows();
   Index cols = m.cols();
 
-  MatrixType m1(rows, cols), m2 = MatrixType::Random(rows, cols), mzero = MatrixType::Zero(rows, cols);
-
-  {
-    int guard = 0;
-    do {
-      m1 = MatrixType::Random(rows, cols);
-    } while ((m1 == mzero || m1 == m2) && (++guard) < 100);
-    VERIFY(guard < 100);
-  }
+  MatrixType m1 = RandomMatrix<MatrixType>(rows, cols, Scalar(0), kMax);
+  MatrixType m2 = RandomMatrix<MatrixType>(rows, cols, Scalar(0), kMax);
 
   // check linear structure
 
-  Scalar s1;
-  {
-    int guard = 0;
-    do {
-      s1 = internal::random<Scalar>();
-    } while (s1 == 0 && (++guard) < 100);
-    VERIFY(guard < 100);
-  }
+  Scalar s1 = internal::random<Scalar>(1, kMax);
 
   VERIFY_IS_EQUAL(-(-m1), m1);
   VERIFY_IS_EQUAL(-m2 + m1 + m2, m1);
@@ -53,46 +40,31 @@ void signed_integer_type_tests(const MatrixType& m) {
 template <typename MatrixType>
 void integer_type_tests(const MatrixType& m) {
   typedef typename MatrixType::Scalar Scalar;
+  constexpr Scalar kMax = (Scalar(1) << ((8 * sizeof(Scalar) - 2) / 2)) - 1;
 
   VERIFY(NumTraits<Scalar>::IsInteger);
   enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };
   VERIFY(int(NumTraits<Scalar>::IsSigned) == is_signed);
 
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
 
   Index rows = m.rows();
   Index cols = m.cols();
 
-  // this test relies a lot on Random.h, and there's not much more that we can do
-  // to test it, hence I consider that we will have tested Random.h
-  MatrixType m1(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), mzero = MatrixType::Zero(rows, cols);
-
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
-  SquareMatrixType identity = SquareMatrixType::Identity(rows, rows), square = SquareMatrixType::Random(rows, rows);
-  VectorType v1(rows), v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows);
-
-  {
-    int guard = 0;
-    do {
-      m1 = MatrixType::Random(rows, cols);
-    } while ((m1 == mzero || m1 == m2) && (++guard) < 100);
-    VERIFY(guard < 100);
-  }
-
-  {
-    int guard = 0;
-    do {
-      v1 = VectorType::Random(rows);
-    } while ((v1 == vzero || v1 == v2) && (++guard) < 100);
-    VERIFY(guard < 100);
-  }
+  MatrixType m1 = RandomMatrix<MatrixType>(rows, cols, Scalar(0), kMax);
+  MatrixType m2 = RandomMatrix<MatrixType>(rows, cols, Scalar(0), kMax);
+  MatrixType m3 = RandomMatrix<MatrixType>(rows, cols, Scalar(0), kMax);
+  SquareMatrixType square = RandomMatrix<SquareMatrixType>(rows, rows, Scalar(0), kMax);
+  VectorType v1 = RandomMatrix<VectorType, Scalar>(rows, Index(1), Scalar(0), NumTraits<Scalar>::highest() / Scalar(2));
 
   VERIFY_IS_APPROX(v1, v1);
   VERIFY_IS_NOT_APPROX(v1, 2 * v1);
-  VERIFY_IS_APPROX(vzero, v1 - v1);
+  VERIFY_IS_APPROX(VectorType::Zero(rows), v1 - v1);
+
   VERIFY_IS_APPROX(m1, m1);
   VERIFY_IS_NOT_APPROX(m1, 2 * m1);
-  VERIFY_IS_APPROX(mzero, m1 - m1);
+  VERIFY_IS_APPROX(MatrixType::Zero(rows, cols), m1 - m1);
 
   VERIFY_IS_APPROX(m3 = m1, m1);
   MatrixType m4;
@@ -113,10 +85,7 @@ void integer_type_tests(const MatrixType& m) {
 
   // check linear structure
 
-  Scalar s1;
-  do {
-    s1 = internal::random<Scalar>();
-  } while (s1 == 0);
+  Scalar s1 = internal::random<Scalar>(1, kMax);
 
   VERIFY_IS_EQUAL(m1 + m1, 2 * m1);
   VERIFY_IS_EQUAL(m1 + m2 - m1, m2);
@@ -134,10 +103,12 @@ void integer_type_tests(const MatrixType& m) {
 
   // check matrix product.
 
-  VERIFY_IS_APPROX(identity * m1, m1);
-  VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);
-  VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square);
-  VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1));
+  if (!NumTraits<Scalar>::IsSigned) {
+    VERIFY_IS_APPROX(SquareMatrixType::Identity(rows, rows) * m1, m1);
+    VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);
+    VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square);
+    VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1));
+  }
 }
 
 template <int>
diff --git a/test/main.h b/test/main.h
index 52c27117b..6cedca562 100644
--- a/test/main.h
+++ b/test/main.h
@@ -902,6 +902,17 @@ void setRandomDataInRange(DataContainer& data_container, typename DataContainer:
 
 using namespace Eigen;
 
+template <typename MatrixType, typename Scalar = typename MatrixType::Scalar>
+MatrixType RandomMatrix(Index rows, Index cols, Scalar min, Scalar max) {
+  MatrixType M = MatrixType(rows, cols);
+  for (Index i = 0; i < rows; ++i) {
+    for (Index j = 0; j < cols; ++j) {
+      M(i, j) = Eigen::internal::random<Scalar>(min, max);
+    }
+  }
+  return M;
+}
+
 /**
  * Set number of repetitions for unit test from input string.
  *
diff --git a/test/product_trmv.cpp b/test/product_trmv.cpp
index 2bbe8ed9a..051d47593 100644
--- a/test/product_trmv.cpp
+++ b/test/product_trmv.cpp
@@ -12,7 +12,6 @@
 template <typename MatrixType>
 void trmv(const MatrixType& m) {
   typedef typename MatrixType::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
 
   Index rows = m.rows();
diff --git a/test/realview.cpp b/test/realview.cpp
index c975284af..0d82ff24b 100644
--- a/test/realview.cpp
+++ b/test/realview.cpp
@@ -12,7 +12,6 @@
 // wrapper that disables array-oriented access to real and imaginary components
 struct TestComplex : public std::complex<float> {
   TestComplex() = default;
-  TestComplex(const TestComplex&) = default;
   TestComplex(std::complex<float> x) : std::complex<float>(x){};
   TestComplex(float x) : std::complex<float>(x){};
 };