diff --git a/.travis.yml b/.travis.yml
index 1bdbd7a69..2fe067094 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,6 +11,10 @@ matrix:
           env:
             - PINTS_UNIT=true
           if: type != cron
+        - python: "2.7.6"
+          env:
+            - PINTS_UNIT=true
+          if: type != cron
         - python: "3.4"
           env:
             - PINTS_UNIT=true
@@ -50,10 +54,17 @@ matrix:
         - python: "3.6"
           if: type == cron
 
-# command to install dependencies
+# Install dependencies
+# Note: Use pip (not apt-get) for Python dependencies
+# Note: Only install normal dependencies for unit tests; these should be tested
+#       without the packages from -dev and -doc!
 install:
+  - pip install --upgrade pip
   - pip install .
-  - pip install -r requirements-dev.txt
+  - pip install -r requirements.txt
+  - if [[ $PINTS_DOCS == true ]]; then pip install -r requirements-docs.txt; fi;
+  - if [[ $PINTS_STYLE == true ]]; then pip install -r requirements-dev.txt; fi;
+  - if [[ $TRAVIS_EVENT_TYPE == 'cron' ]]; then pip install -r requirements-dev.txt; fi;
   - if [[ $PINTS_COVER == true ]]; then pip install coverage codecov; fi;
 
 before_script:
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index b4d12b204..3acfe66e4 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -241,6 +241,12 @@ Note that these files must be kept in sync with
 
 The requirements files link to each other, so that calling `$ pip install -r requirements-dev.txt` will install everything listed in `requirements.txt` and `requirements-docs.txt` as well.
 
+It's always worth using an up-to-date version of pip. On older systems especially, having an up-to-date pip will prevent all kinds of version incompatibility issues:
+
+```
+$ pip install --upgrade pip
+```
+
 ### Travis CI
 
 All committed code is tested using [Travis CI](https://travis-ci.org/), tests are published on https://travis-ci.org/pints-team/pints.
diff --git a/README.md b/README.md
index 44fc8b42e..78a1986f0 100644
--- a/README.md
+++ b/README.md
@@ -34,7 +34,13 @@ You'll need the following requirements:
 - Python 2.7 or Python 3.4+
 - Python libraries: `cma` `numpy` `matplotlib` `scipy`
 
-These will be installed automatically if you go to the directory you downloaded pints to, and run
+These can easily be installed using `pip`. To do this, first make sure you have the latest version of pip installed:
+
+```
+$ pip install --upgrade pip
+```
+
+Then navigate to the path where you downloaded Pints to, and install both Pints and its dependencies by typing:
 
 ```
 $ pip install .
diff --git a/pints/noise.py b/pints/noise.py
index cbef0f0c4..ed5398d73 100644
--- a/pints/noise.py
+++ b/pints/noise.py
@@ -29,8 +29,8 @@ def independent(sigma, shape):
         noisy_values = values + noise.independent(5, values.shape)
 
     """
-    # Don't test sigma/shape: handled by numpy for higher-dimensions etc.!
 
+    # Don't test sigma/shape: handled by numpy for higher-dimensions etc.!
     return np.random.normal(0, sigma, shape)
 
 
@@ -75,7 +75,11 @@ def ar1(rho, sigma, n):
         return np.array([])
 
     # Generate noise
-    v = np.random.normal(0, sigma * np.sqrt(1 - rho**2), n)
+    s = sigma * np.sqrt(1 - rho**2)
+    if s == 0:
+        v = np.zeros(n)
+    else:
+        v = np.random.normal(0, s, n)
     v[0] = np.random.rand()
     for t in range(1, n):
         v[t] += rho * v[t - 1]
diff --git a/pints/tests/test_noise.py b/pints/tests/test_noise.py
index 5ac777c0c..949c01e65 100755
--- a/pints/tests/test_noise.py
+++ b/pints/tests/test_noise.py
@@ -41,7 +41,7 @@ def test_independent_noise(self):
         self.assertRaises(ValueError, pn.independent, -1, clean.shape)
 
         # Shape must be a nice shape (handled by numpy)
-        self.assertRaises(TypeError, pn.independent, 0, 'hello')
+        self.assertRaises(TypeError, pn.independent, 1, 'hello')
 
     def test_ar1(self):