diff --git a/tox.ini b/tox.ini
index 06d4ab0..ea8e426 100644
--- a/tox.ini
+++ b/tox.ini
@@ -3,7 +3,7 @@ envlist = py{27,34,35,36,37,38}-{with,without}_coverage-{,appveyor}
 
 [testenv]
 install_command =
-    pip install -vvv {opts} {packages}
+    {envpython} -m pip install -vvv {opts} {packages}
 ; setenv =
 ;    ; The following two flags are a workaround for an issue with building
 ;    ; Python extensions on OSX with xcode 5.1.
@@ -17,6 +17,12 @@ deps =
     py{27}: unittest2==1.1.0
     py{27}: mock==1.3.0
     py{27}: biopython<=1.76
+    py{34}: setuptools<44
+    py{34}: pip<19.2
+    ; biopython 1.74 has numpy as a dependency, but the version must be
+    ; limited to work on Python 3.4. (i.e `pip install numpy` no longer works
+    ; on Python 3.4!)
+    py{34}: numpy<1.16
     py{34}: biopython<=1.74
     py{35}: biopython<=1.76
     py{36,37,38}: biopython