diff --git a/src/solvers.jl b/src/solvers.jl
index 819361a109b..dbb28ef6a83 100644
--- a/src/solvers.jl
+++ b/src/solvers.jl
@@ -992,8 +992,12 @@ function conicdata(m::Model)
             for i in 1:n, j in 1:(i-1)
                 collect_expr!(m, tmprow, con.terms[i,j] - con.terms[j,i])
                 nnz = tmprow.nnz
-                # if the symmetry-enforcing row is empty, just drop it
-                if nnz == 0
+                # if the symmetry-enforcing row is empty or has only tiny coefficients due to unintended numerical asymmetry, drop it
+                largestabs = 0.0
+                for k in 1:nnz
+                    largestabs = max(largestabs,abs(tmpelts[tmpnzidx[k]]))
+                end
+                if largestabs < 1e-10
                     numDroppedSym += 1
                     continue
                 end
@@ -1005,7 +1009,9 @@ function conicdata(m::Model)
                 append!(V, tmpelts[indices])
                 b[c] = 0
             end
-            push!(con_cones, (:Zero, sym_start:c))
+            if c >= sym_start
+                push!(con_cones, (:Zero, sym_start:c))
+            end
             constr_dual_map[numLinRows + numBounds + numNormRows + length(m.sdpconstr) + sdpidx] = collect(sym_start:c)
             @assert length(syms) == length(sym_start:c)
         else
diff --git a/test/sdp.jl b/test/sdp.jl
index fd2b8350f14..2b8b2687c08 100644
--- a/test/sdp.jl
+++ b/test/sdp.jl
@@ -173,13 +173,14 @@ ispsd(x::JuMP.JuMPArray) = ispsd(x.innerArray)
         @test isapprox(getobjectivevalue(m), 1.293, atol=1e-2)
     end
 
-    @testset "Trivial symmetry constraints are removed (#766)" begin
+    @testset "Trivial symmetry constraints are removed (#766, #972)" begin
         q = 2
         m = 3
         angles1 = linspace(3*pi/4, pi, m)
         angles2 = linspace(0, -pi/2, m)
-        V = [3.*cos(angles1)' 1.5.*cos(angles2)';
-             3.*sin(angles1)' 1.5.*sin(angles2)']
+        V = [3.*cos.(angles1)' 1.5.*cos.(angles2)';
+             3.*sin.(angles1)' 1.5.*sin.(angles2)']
+        V[abs.(V) .< 1e-10] = 0.0
         p = 2*m
         n = 100
 
@@ -193,10 +194,11 @@ ispsd(x::JuMP.JuMPArray) = ispsd(x.innerArray)
         end
         f, A, b, var_cones, con_cones = JuMP.conicdata(mod)
         @test length(f) == 8
-        @test size(A) == (23,8)
-        @test length(b) == 23
+        @test size(A) == (21,8)
+        @test minimum(abs.(nonzeros(A))) > 0.01
+        @test length(b) == 21
         @test var_cones == [(:Free,[1,2,3,4,5,6,7,8])]
-        @test con_cones == [(:NonNeg,[1]),(:NonPos,[2,3,4,5,6,7,8,9]),(:SDP,10:15),(:Zero,16:16),(:SDP,17:22),(:Zero,23:23)]
+        @test con_cones == [(:NonNeg,[1]),(:NonPos,[2,3,4,5,6,7,8,9]),(:SDP,10:15),(:SDP,16:21)]
     end
 
     # Adapt SDP atom tests from Convex.jl: